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University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
FAX: +1 801 581 4148,
e-mail: \path|[email protected]|,
\path|[email protected]|,
\path|[email protected]| (Internet),
URL: \path|https://www.math.utah.edu/~beebe/|"}
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@TechReport{Fox:1941:NUR,
author = "L. Fox and R. V. Southwell",
title = "Note on the use of relaxation methods for the
computation of two-dimensional stress systems",
type = "Report",
number = "E. F. 466",
institution = "Aeronautical Research Committee, Structure
subcommittee, Strut 512",
address = "????",
year = "1941",
bibdate = "Tue Nov 14 07:13:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
note = "This is Leslie Fox's first publication.",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Allen:1942:RMA,
author = "D. N. de G. Allen and L. Fox and H. Motz and R. V.
Southwell",
title = "Relaxation methods applied to engineering problems.
{VII C}. {Free} transverse vibrations of membranes,
with an application (by analogy) to two-dimensional
oscillations in an electro-magnetic system",
journal = "Philosophical Transactions of the Royal Society,
Series C",
volume = "1",
number = "??",
pages = "85--97",
month = "????",
year = "1942",
bibdate = "Tue Nov 14 07:26:48 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
remark = "TO DO: Find journal correct name and Web site and
remaining metadata.",
}
@Article{Christopherson:1942:RMA,
author = "D. G. Christopherson and L. Fox and J. R. Green and F.
S. Shaw and R. V. Southwell",
title = "Relaxation methods applied to engineering problems,
{VII B}, The elastic stability of plane frameworks and
of flat plating",
journal = "Philosophical Transactions of the Royal Society,
Series C",
volume = "1",
number = "??",
pages = "57--83",
month = "????",
year = "1942",
bibdate = "Tue Nov 14 07:19:02 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
remark = "TO DO: Find journal correct name and Web site and
remaining metadata.",
}
@PhdThesis{Fox:1942:RMA,
author = "Leslie Fox",
title = "Relaxation methods applied to problems of plane stress
and strain",
type = "{D.Phil.} dissertation",
school = "University of Oxford",
address = "Oxford, UK",
pages = "79",
year = "1942",
bibdate = "Mon Nov 13 13:40:21 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
URL = "https://www.proquest.com/pqdtglobal/docview/2497394794",
acknowledgement = ack-nhfb,
advisor = "Sir Richard Vynne Southwell",
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@TechReport{Fox:1942:STB,
author = "L. Fox and R. V. Southwell",
title = "On the stressing of tapered box beams",
type = "Report",
number = "??",
institution = "Aeronautical Research Committee, Structure
subcommittee 6034, Strut 598",
address = "????",
year = "1942",
bibdate = "Tue Nov 14 07:16:34 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Allen:1943:RMA,
author = "D. N. de G. Allen and L. Fox and R. V. Southwell",
title = "Relaxation methods applied to engineering problems.
{VII D}. {Stress} distributions in elastic solids of
revolution",
journal = "Philosophical Transactions of the Royal Society,
Series C",
volume = "1",
number = "??",
pages = "99--135",
month = "????",
year = "1943",
bibdate = "Tue Nov 14 07:28:39 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
remark = "TO DO: Find journal correct name and Web site and
remaining metadata.",
}
@Article{Fox:1944:FGT,
author = "L. Fox and R. V. Southwell",
title = "On the flow of gas through a nozzle with velocities
exceeding the speed of sound",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "183",
number = "992",
pages = "38--54",
month = aug,
year = "1944",
CODEN = "PRLAAZ",
DOI = "https://doi.org/10.1098/rspa.1944.0020",
ISSN = "0080-4630 (print), 2053-9169 (electronic)",
ISSN-L = "0080-4630",
bibdate = "Tue Nov 14 07:32:02 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "Proc Roy Soc A",
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Proceedings of the Royal Society of London. Series A,
Mathematical and physical sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/",
}
@Article{Fox:1944:SRM,
author = "L. Fox",
title = "Solution by relaxation methods of plane potential
problems with mixed boundary conditions",
journal = j-QUART-APPL-MATH,
volume = "2",
number = "3",
pages = "251--257",
month = "????",
year = "1944",
CODEN = "QAMAAY",
DOI = "https://doi.org/10.1090/qam/10679",
ISSN = "0033-569X (print), 1552-4485 (electronic)",
ISSN-L = "0033-569X",
MRclass = "65.0X",
MRnumber = "10679",
MRreviewer = "D. Moskovitz",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Quarterly of Applied Mathematics",
journal-URL = "http://dl.acm.org/citation.cfm?id=J641;
http://www.ams.org/journals/qam",
}
@Article{Allen:1945:RMAc,
author = "D. N. de G. Allen and L. Fox and H. Motz and R. V.
Southwell",
title = "Relaxation methods applied to engineering problems.
{VII C}. {Free} transverse vibrations of membranes,
with an application (by analogy) to two-dimensional
oscillations in an electro-magnetic system",
journal = j-PHILOS-TRANS-R-SOC-LOND-SER-A,
volume = "239",
number = "810",
pages = "488--500",
month = oct,
year = "1945",
CODEN = "PTRMAD, PTMSFB",
DOI = "https://doi.org/10.1098/rsta.1945.0003",
ISSN = "0080-4614 (print), 2054-0272 (electronic)",
ISSN-L = "1364-503X",
MRclass = "73.2X",
MRnumber = "14312",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Philosophical Transactions of the Royal Society of
London. Series A. Mathematical and Physical Sciences",
journal-URL = "http://rsta.royalsocietypublishing.org/",
}
@Article{Allen:1945:RMAd,
author = "D. N. de G. Allen and L. Fox and R. V. Southwell",
title = "Relaxation methods applied to engineering problems.
{VII D}. {Stress} distributions in elastic solids of
revolution",
journal = j-PHILOS-TRANS-R-SOC-LOND-SER-A,
volume = "239",
number = "810",
pages = "501--537",
month = oct,
year = "1945",
CODEN = "PTRMAD, PTMSFB",
DOI = "https://doi.org/10.1098/rsta.1945.0004",
ISSN = "0080-4614 (print), 2054-0272 (electronic)",
ISSN-L = "1364-503X",
MRclass = "73.2X",
MRnumber = "14313",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Philosophical Transactions of the Royal Society of
London. Series A. Mathematical and Physical Sciences",
journal-URL = "http://rsta.royalsocietypublishing.org/",
}
@Article{Christopherson:1945:RMA,
author = "D. G. Christopherson and L. Fox and J. R. Green and F.
S. Shaw and R. V. Southwell",
title = "Relaxation methods applied to engineering problems.
{VII B}. {The} elastic stability of plane frameworks
and of flat plating",
journal = j-PHILOS-TRANS-R-SOC-LOND-SER-A,
volume = "239",
number = "810",
pages = "461--487",
month = oct,
year = "1945",
CODEN = "PTRMAD, PTMSFB",
DOI = "https://doi.org/10.1098/rsta.1945.0002",
ISSN = "0080-4614 (print), 2054-0272 (electronic)",
ISSN-L = "1364-503X",
MRclass = "73.2X",
MRnumber = "14311",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Philosophical Transactions of the Royal Society of
London. Series A. Mathematical and Physical Sciences",
journal-URL = "http://rsta.royalsocietypublishing.org/",
}
@Article{Fox:1945:RMA,
author = "L. Fox and R. V. Southwell",
title = "Relaxation methods applied to engineering problems.
{VII A}. {Biharmonic} analysis as applied to the
flexure and extension of flat elastic plates",
journal = j-PHILOS-TRANS-R-SOC-LOND-SER-A,
volume = "239",
number = "810",
pages = "419--460",
month = oct,
year = "1945",
CODEN = "PTRMAD, PTMSFB",
DOI = "https://doi.org/10.1098/rsta.1945.0001",
ISSN = "0080-4614 (print), 2054-0272 (electronic)",
ISSN-L = "1364-503X",
MRclass = "73.2X",
MRnumber = "14310",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Philosophical Transactions of the Royal Society of
London. Series A. Mathematical and Physical Sciences",
journal-URL = "http://rsta.royalsocietypublishing.org/",
}
@TechReport{Fox:1945:SIE,
author = "L. Fox and others",
title = "Solution of integral equations occurring in an
aerodynamical problem",
type = "Report",
number = "SRE/ACS 89",
institution = "Admiralty Computing Service (S.R.E. Dept.)",
address = "Bath, UK",
pages = "????",
year = "1945",
bibdate = "Tue Nov 14 14:41:23 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
remark = "TO DO: find correct author list: cited in \cite[p.
36]{Fox:1987:ENA}.",
}
@TechReport{Fox:1945:TF,
author = "L. Fox and others",
title = "Tabulation of the function {$ f(x, y) = \int_0^\infty
\exp ( - k)(J_0 (k x) \cosh (k y) - 1) \cosech (k) \, d
k $}",
type = "Report",
number = "SRE/ACS 47",
institution = "Admiralty Computing Service (S.R.E. Dept.)",
address = "Bath, UK",
pages = "????",
year = "1945",
bibdate = "Tue Nov 14 14:41:23 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
remark = "TO DO: find correct author list: cited in \cite[p.
36]{Fox:1987:ENA}.",
}
@TechReport{Fox:1946:CST,
author = "L. Fox",
title = "Computation of the stresses in a two-layer system
resulting from uniform loading symmetrically applied to
the upper surface",
type = "Road Research Laboratory Report",
number = "RN/723",
institution = pub-HMSO,
address = pub-HMSO:adr,
year = "1946",
bibdate = "Tue Nov 14 07:39:57 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Fox:1946:SHT,
author = "L. Fox and R. V. Southwell",
title = "On the stresses in hooks, and their determination by
relaxation methods",
journal = "Inst Mech Eng Appl Mech Proc",
volume = "155",
number = "??",
pages = "1--19",
month = "????",
year = "1946",
bibdate = "Tue Nov 14 07:37:12 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Fox:1947:MBC,
author = "L. Fox",
title = "Mixed boundary conditions in the relaxational
treatment of biharmonic problems (plane strain or
stress)",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "189",
number = "1019",
pages = "535--543",
month = jun,
year = "1947",
CODEN = "PRLAAZ",
DOI = "https://doi.org/10.1098/rspa.1947.0056",
ISSN = "0962-8444 (print), 2053-9177 (electronic)",
ISSN-L = "0962-8444",
MRclass = "65.0X",
MRnumber = "20347",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical, Physical and Engineering Sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/",
}
@Article{Fox:1947:SIU,
author = "L. Fox",
title = "Some improvements in the use of relaxation methods for
the solution of ordinary and partial differential
equations",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "190",
number = "1020",
pages = "31--59",
month = jun,
year = "1947",
CODEN = "PRLAAZ",
DOI = "https://doi.org/10.1098/rspa.1947.0060",
ISSN = "0962-8444 (print), 2053-9177 (electronic)",
ISSN-L = "0962-8444",
MRclass = "65.0X",
MRnumber = "21737",
MRreviewer = "W. E. Milne",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical, Physical and Engineering Sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/",
}
@TechReport{Fox:1948:CTS,
author = "L. Fox",
title = "Computation of traffic stresses in a simple road
structure",
type = "Road Res Lab Tech Paper",
number = "9",
institution = pub-HMSO,
address = pub-HMSO:adr,
year = "1948",
bibdate = "Tue Nov 14 07:49:57 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Fox:1948:NSA,
author = "L. Fox and H. D. Huskey and J. H. Wilkinson",
title = "Notes on the Solution of Algebraic Linear Simultaneous
Equations",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "1",
number = "1",
pages = "149--173",
month = jan,
year = "1948",
CODEN = "QJMMAV",
DOI = "https://doi.org/10.1093/qjmam/1.1.149",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
MRclass = "65.0X",
MRnumber = "MR0026421 (10,152i 26421)",
MRreviewer = "E. Bodewig",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
abstract = "In this paper four methods of solving simultaneous
equations and inverting matrices are described from the
viewpoint of the practical computer. The first three
methods can be performed on ordinary desk calculating
machines; the fourth uses Hollerith punched card
equipment. The desk methods considered are the method
of elimination or pivotal condensation, the method of
orthogonal vectors, and the method of Choleski. The
elimination method is, with slight variants, the simple
method taught at school, used in such a way that
solutions are obtained with the maximum possible speed
and accuracy. In the method of orthogonal vectors,
applicable only to symmetric matrices, a new set of
variables is chosen in such a way that the matrix is
transformed to a diagonal form, from which the solution
of equations or the inverse of the matrix is
immediately obtainable. The Choleski method, applied
here again only to symmetric matrices, expresses the
square matrix as the product of two triangular
matrices, the reciprocation of which is a relatively
simple operation. This method is quicker and more
accurate than the others and can be used, with slight
modifications, in the case of unsymmetric matrices. The
procedure used with punched card equipment is
essentially a mechanization of the elimination method,
with a considerable advantage in speed over the
corresponding desk method.",
acknowledgement = ack-nhfb,
author-dates = "James H. Wilkinson (27 September 1919--5 October
1986); Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "The Quarterly Journal of Mechanics and Applied
Mathematics",
journal-URL = "http://qjmam.oxfordjournals.org/content/by/year",
remark = "The survey paper by Gene H. Golub and Dianne P.
O'Leary, ``Some History of the Conjugate Gradient and
{Lanczos} Algorithms: 1948--1976'', SIAM Review {\bf
31}(1) 50--102 March 1989, doi:10.1137/1031003, (entry
Golub:1989:SHC in golub-gene-h.bib) credits this paper
as the origin of the conjugate gradient method that was
later, and independently, developed in depth in 1951 by
Eduard Stiefel and Magnus Hestenes and published in
their joint paper, ``Methods of Conjugate Gradients for
Solving Linear Systems'' Journal of Research of the
National Bureau of Standards {\bf 49}(6) 409--436
December 1952, doi:10.6028/jres.049.044 (entry
Hestenes:1952:MCG in hestenes-magnus-r.bib and
stiefel-eduard.bib).",
}
@TechReport{Fox:1948:SAL,
author = "L. Fox and H. D. Huskey and J. H. Wilkinson",
title = "The Solution of Algebraic Linear Simultaneous
Equations by Punched Card Methods",
type = "Maths",
institution = inst-NPL,
address = inst-NPL:adr,
year = "1948",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Fox:1948:SAR,
author = "L. Fox",
title = "A short account of relaxation methods",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "1",
number = "1",
pages = "253--280",
month = jan,
year = "1948",
CODEN = "QJMMAV",
DOI = "https://doi.org/10.1093/qjmam/1.1.253",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
MRclass = "65.0X",
MRnumber = "29270",
MRreviewer = "E. Bodewig",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "The Quarterly Journal of Mechanics and Applied
Mathematics",
journal-URL = "http://qjmam.oxfordjournals.org/content/by/year",
}
@Article{Fox:1949:SNM,
author = "L. Fox and E. T. Goodwin",
title = "Some new methods for the numerical integration of
ordinary differential equations",
journal = j-PROC-CAMBRIDGE-PHIL-SOC,
volume = "45",
number = "3",
pages = "373--388",
month = jul,
year = "1949",
CODEN = "PCPSA4",
DOI = "https://doi.org/10.1017/s0305004100025007",
ISSN = "0008-1981",
ISSN-L = "0008-1981",
MRclass = "65.0X",
MRnumber = "30315",
MRreviewer = "H. O. Hartley",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Proceedings of the Cambridge Philosophical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP",
}
@Article{Fox:1949:SRM,
author = "L. Fox and E. T. Goodwin",
title = "The solution by relaxation methods of ordinary
differential equations",
journal = j-MATH-PROC-CAMB-PHILOS-SOC,
volume = "45",
number = "1",
pages = "50--68",
month = jan,
year = "1949",
CODEN = "MPCPCO",
DOI = "https://doi.org/10.1017/S0305004100000438",
ISSN = "0305-0041 (print), 1469-8064 (electronic)",
ISSN-L = "0305-0041",
MRclass = "65.0X",
MRnumber = "28688",
MRreviewer = "S. C. van Veen",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Mathematical Proceedings of the Cambridge
Philosophical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP",
}
@Article{Foks:1950:NSS,
author = "L. Foks and H. D. Haski and D{\v{z}}. H. Vilkinson",
title = "Notes on the solution of simultaneous linear algebraic
equations",
journal = "Uspekhi Matematicheskikh Nauk (N.S.)",
volume = "5",
number = "3(37)",
pages = "60--86",
year = "1950",
CODEN = "UMANA5",
ISSN = "0042-1316 (print), 2305-2872 (electronic)",
ISSN-L = "0042-1316",
MRclass = "65.0X",
MRnumber = "35512",
bibdate = "Tue Nov 14 16:25:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Russian translation of \cite{Fox:1948:NSA}.",
acknowledgement = ack-nhfb,
ajournal = "Uspehi Matem. Nauk (N.S.)",
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Uspekhi Matematicheskikh Nauk (N.S.)",
remark = "Journal published 1946--1954; no online archive.
https://cassi.cas.org seems to indicate same CODEN and
ISSN for old and new series.",
}
@Article{Fox:1950:NSE,
author = "L. Fox",
title = "The numerical solution of elliptic differential
equations when the boundary conditions involve a
derivative",
journal = j-PHILOS-TRANS-R-SOC-LOND-SER-A,
volume = "242",
number = "849",
pages = "345--378",
month = may,
year = "1950",
CODEN = "PTRMAD, PTMSFB",
DOI = "https://doi.org/10.1098/rsta.1950.0004",
ISSN = "0080-4614 (print), 2054-0272 (electronic)",
ISSN-L = "1364-503X",
MRclass = "65.0X",
MRnumber = "35525",
MRreviewer = "H. O. Hartley",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Philosophical Transactions of the Royal Society of
London. Series A. Mathematical and Physical Sciences",
journal-URL = "http://rsta.royalsocietypublishing.org/",
}
@Article{Fox:1950:NSO,
author = "L. Fox",
title = "The numerical solution of ordinary differential
equations",
journal = "Proc I.C.M.",
volume = "1",
number = "??",
pages = "??--??",
month = "????",
year = "1950",
bibdate = "Tue Nov 14 07:57:57 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Fox:1950:PMS,
author = "L. Fox",
title = "Practical Methods for the Solution of Linear Equations
and the Inversion of Matrices",
journal = j-J-R-STAT-SOC-SER-B-METHODOL,
volume = "12",
number = "1",
pages = "120--136",
month = "????",
year = "1950",
CODEN = "JSTBAJ",
DOI = "https://doi.org/10.2307/2983838",
ISSN = "0035-9246",
ISSN-L = "0035-9246",
MRclass = "65.0X",
MRnumber = "39371",
MRreviewer = "F. J. Murray",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "http://www.jstor.org/stable/i349691;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/jrss-b.bib",
URL = "http://links.jstor.org/sici?sici=0035-9246(1950)12:1<120:PMFTSO>2.0.CO;2-W&origin=MSN;
http://www.jstor.org/stable/2983838",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Journal of the Royal Statistical Society. Series B
(Methodological)",
journal-URL = "http://www.jstor.org/journals/00359246.html",
}
@Article{Fox:1951:CLS,
author = "L. Fox and W. E. A. Acum",
title = "Computation of load stresses in a three-layer elastic
system",
journal = "Geotechnique Inst Civ Eng",
volume = "??",
number = "??",
pages = "293--300",
month = "????",
year = "1951",
bibdate = "Tue Nov 14 08:00:32 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Fox:1951:MPM,
author = "L. Fox and J. G. Hayes",
title = "More Practical Methods for the Inversion of Matrices",
journal = j-J-R-STAT-SOC-SER-B-METHODOL,
volume = "13",
number = "1",
pages = "83--91",
month = "????",
year = "1951",
CODEN = "JSTBAJ",
DOI = "https://doi.org/10.2307/2983969",
ISSN = "0035-9246",
ISSN-L = "0035-9246",
MRclass = "65.0X",
MRnumber = "48158",
MRreviewer = "G. E. Forsythe",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "http://www.jstor.org/stable/i349693;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/jrss-b.bib",
URL = "http://links.jstor.org/sici?sici=0035-9246(1951)13:1<83:MPMFTI>2.0.CO;2-V&origin=MSN;
http://www.jstor.org/stable/2983969",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Journal of the Royal Statistical Society. Series B
(Methodological)",
journal-URL = "http://www.jstor.org/journals/00359246.html",
}
@Article{Fox:1951:NNAa,
author = "L. Fox",
title = "Notes on Numerical Analysis --- 4: Relaxation and
Step-by-Step Methods (in Automatic Computing Machinery;
Discussions)",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "5",
number = "34",
pages = "92--95",
month = apr,
year = "1951",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-51-99434-3",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Fox:1951:NNAb,
author = "L. Fox and J. C. P. Miller",
title = "Notes on Numerical Analysis --- 5: Table-Making for
Large Arguments. The Exponential Integral (in
{Automatic Computing Machinery})",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "5",
number = "35",
pages = "163--166",
month = jul,
year = "1951",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-51-99425-2",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Fox:1952:EML,
author = "L. Fox",
title = "Escalator methods for latent roots",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "5",
number = "2",
pages = "178--190",
year = "1952",
CODEN = "QJMMAV",
DOI = "https://doi.org/10.1093/qjmam/5.2.178",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
MRclass = "65.0X",
MRnumber = "48912",
MRreviewer = "B. Friedman",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "The Quarterly Journal of Mechanics and Applied
Mathematics",
journal-URL = "http://qjmam.oxfordjournals.org/content/by/year",
}
@Article{Fox:1953:NSN,
author = "L. Fox and E. T. Goodwin",
title = "The numerical solution of non-singular linear integral
equations",
journal = j-PHILOS-TRANS-R-SOC-LOND-SER-A,
volume = "245",
number = "902",
pages = "501--534",
month = feb,
year = "1953",
CODEN = "PTRMAD, PTMSFB",
DOI = "https://doi.org/10.1098/rsta.1953.0005",
ISSN = "0080-4614 (print), 2054-0272 (electronic)",
ISSN-L = "1364-503X",
MRclass = "65.0X",
MRnumber = "54355",
MRreviewer = "H. B{{\"u}}ckner",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Philosophical Transactions of the Royal Society of
London. Series A. Mathematical and Physical Sciences",
journal-URL = "http://rsta.royalsocietypublishing.org/",
remark = "Title in \cite{Anonymous:1992:LF} is incorrect. I
cannot find the bad title in Web searches: was it ever
published?",
xxtitle = "Application of digital computing methods to mass
spectrometry analysis",
}
@Article{Fox:1953:ULI,
author = "L. Fox",
title = "The Use of Large Intervals in Finite-Difference
Equations",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "7",
number = "41",
pages = "14--18",
month = jan,
year = "1953",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1953-0052889-5",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "65.0X",
MRnumber = "52889",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Fox:1954:NNI,
author = "L. Fox",
title = "A note on the numerical integration of first-order
differential equations",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "7",
number = "3",
pages = "367--378",
year = "1954",
CODEN = "QJMMAV",
DOI = "https://doi.org/10.1093/qjmam/7.3.367",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
MRclass = "65.0X",
MRnumber = "69591",
MRreviewer = "W. E. Milne",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "The Quarterly Journal of Mechanics and Applied
Mathematics",
journal-URL = "http://qjmam.oxfordjournals.org/content/by/year",
}
@Book{Fox:1954:PMS,
author = "L. Fox",
title = "Practical Methods for the Solution of Linear Equations
and the Inversion of Matrices",
volume = "39",
publisher = pub-USGPO,
address = pub-USGPO:adr,
pages = "1--54",
year = "1954",
bibdate = "Tue Nov 14 15:11:17 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
series = "NBS Applied Mathematics Series",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@InCollection{Fox:1954:PSL,
author = "L. Fox",
booktitle = "Contributions to the solution of systems of linear
equations and the determination of eigenvalues",
title = "Practical solution of linear equations and inversion
of matrices",
volume = "39",
publisher = pub-USGPO,
address = pub-USGPO:adr,
pages = "1--54",
year = "1954",
MRclass = "65.0X",
MRnumber = "65259",
MRreviewer = "A. S. Householder",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
series = "National Bureau of Standards Applied Mathematics
Series",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Fox:1954:STB,
author = "L. Fox",
title = "A Short Table for {Bessel} Functions of Integer Orders
and Large Arguments",
volume = "3",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "28",
year = "1954",
MRclass = "65.0X",
MRnumber = "65245",
MRreviewer = "R. C. Archibald",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
series = "Royal Society Shorter Mathematical Tables",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Fox:1956:UCM,
author = "L. Fox",
title = "The Use and Construction of Mathematical Tables",
volume = "1",
publisher = pub-HMSO,
address = pub-HMSO:adr,
pages = "iv + 60",
month = jun,
year = "1956",
bibdate = "Tue Nov 14 08:07:39 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
series = "N.P.L. Mathematical Tables",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
tableofcontents = "The use of mathematical tables \\
Derivation of formulae and analysis of error \\
The construction of mathematical tables",
}
@Article{Fox:1957:BVT,
author = "L. Fox and A. R. Mitchell",
title = "Boundary-value techniques for the numerical solution
of initial-value problems in ordinary differential
equations",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "10",
number = "2",
pages = "232--243",
year = "1957",
CODEN = "QJMMAV",
DOI = "https://doi.org/10.1093/qjmam/10.2.232",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
MRclass = "65.3X",
MRnumber = "93025",
MRreviewer = "J. Kuntzmann",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "The Quarterly Journal of Mechanics and Applied
Mathematics",
journal-URL = "http://qjmam.oxfordjournals.org/content/by/year",
}
@Book{Fox:1957:MCM,
author = "L. Fox and E. T. Goodwin and J. G. L. Michel and F. W.
J. Olver and J. H. Wilkinson",
title = "Modern Computing Methods",
volume = "16",
publisher = pub-HMSO,
address = pub-HMSO:adr,
pages = "vi + 128",
year = "1957",
LCCN = "QA297 .T4",
bibdate = "Tue Nov 07 08:00:14 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib",
series = "NPL Notes on Applied Science",
acknowledgement = ack-nhfb,
author-dates = "Frank William John Olver (15 December 1924--23 April
2013); James H. Wilkinson (27 September 1919--5 October
1986); Leslie Fox (30 September 1918--1 August 1992)",
xxnote = "TO DO: Check author order; library catalog entries
lack the author list and table of contents. John
Crank's review (doi:10.1088/0031-9112/8/11/010) says
``It seems a pity that the contributors remain
anonymous. Presumably they were not disguised when they
delivered the lectures on which the book is based.''",
}
@Book{Fox:1957:NST,
author = "L. Fox",
title = "The Numerical Solution of Two-point Boundary Problems
in Ordinary Differential Equations",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xi + 371",
year = "1957",
MRclass = "65.00",
MRnumber = "102178",
MRreviewer = "Z. Kopal",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
note = "Reprinted in \cite{Fox:1990:NST}.",
series = "Monographs on Numerical Analysis",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
series-editor = "E. T. (Eric Thomson) Goodwin and D. R. Hartree and
Leslie Fox",
shorttableofcontents = "1. Introduction / 2 \\
2. Finite Differences and Finite-Difference / 6 \\
3. The Solution of Algebraic Equations / 34 \\
4. Second-Order Equations / 67 \\
5. First-Order Equations / 106 \\
6. Equations of Higher Orders / 128 \\
7. Eigenvalue Problems 159 / 159 \\
8. Initial-Value Techniques For Boundary-Value Problems
/ 228 \\
9. Accuracy and Precision of Boundary-Value Methods /
274 \\
10. Miscellaneous Methods and Comments / 326 \\
Index / 365",
tableofcontents = "1. Introduction \\
Definitions / 1 \\
Analytical and numerical solutions / 2 \\
Boundary conditions and initial conditions / 3 \\
Additional notes and bibliography / 5 \\
2, Finite Differences and Finite-Difference Equations
\\
Introduction / 6 \\
Differences / 6 \\
Operators / 7 \\
Interpolation 9 / 17 \\
Differentiation / 10 \\
Integration / 12 \\
Sums and sum operators / 13 \\
Relations between formulae / 17 \\
The difference correction / 17 \\
Tables of formulae / 18 \\
The practical application of finite-difference
equations / 20 \\
Convergent differences / 22 \\
Numerical applications. Accuracy and precision / 24 \\
Divergent differences / 27 \\
Recapitulation / 30 \\
Lagrangian formulae / 31 \\
Additional notes and bibliography / 32 \\
3. The Solution of Algebraic Equations \\
Differential equations and algebraic equations / 34 \\
The difference correction / 35 \\
Linear algebraic equations. Iterative methods / 36 \\
The relaxation method / 36 \\
Notes on relaxation / 39 \\
Condition and convergence / 42 \\
Direct methods / 45 \\
Non-linear equations / 47 \\
Solution of simultaneous finite-difference equations /
49 \\
Relaxation: a computational arrangement for difference
equations / 50 \\
Relaxation: second-order equations / 51 \\
Relaxation: simultaneous second-order equations / 56
\\
Relaxation: fourth-order equations / 57 \\
Relaxation: equations of odd order / 58 \\
Direct methods: second-order equations / 59 \\
Direct methods: simultaneous second-order equations /
61 \\
Direct methods: fourth-order equations / 62 \\
Direct methods: equations of odd order / 63 \\
General comments / 64 \\
Additional notes and bibliography / 67 \\
4. Second-Order Equations \\
Introduction / 67 \\
Finite-difference equations / 67 \\
Simple examples: boundary values specified / 68 \\
Boundary condition involving derivative. Simple example
/ 74 \\
An alternative to the difference correction. Iteration
/ 79 \\
Example / 80 \\
Simultaneous second-order equations / 81 \\
Non-linear equations / 84 \\
Iterative methods. Examples / 86 \\
The `$\eta$ method / 87 \\
Boundary condition at infinity / 91 \\
Mixed boundary conditions / 93 \\
Change of interval / 94 \\
Singularities / 98 \\
The use of Taylor's series for boundary conditions /
101 \\
Additional notes and bibliography / 103 \\
5. First-Order Equations \\
Introduction / 106 \\
Finite-difference equations and boundary conditions /
106 \\
Compatibility of boundary values. Simple examples / 107
\\
A practical example / 111 \\
A smaller difference correction 113 Alternative methods
/ 113 \\
Method 1 / 114 \\
Method 2 / 116 \\
Method 3 / 117 \\
Solution of the linear equations / 117 \\
Normalization / 118 \\
Transformation to second-order differential equation /
119 \\
Choice of method. Illustrative example / 122 \\
Additional notes and bibliography / 125 \\
6. Equations of Higher Orders \\
Fourth-order linear equations / 128 \\
General boundary conditions / 128 \\
Special boundary conditions / 130 \\
Method of solution. Simple example / 131 \\
Other methods of solution / 134 \\
Other boundary conditions / 137 \\
Third-order equations / 138 \\
Oscillation. / 138 \\
Example / 138 \\
Discussion of oscillation / 140 \\
Removal of oscillation / 141 \\
Example / 143 \\
Transformation to second-order equation / 144 \\
Example / 145 \\
Other transformations / 148 \\
Equations of order higher than the fourth, Non-linear
equations / 150 \\
Matrix solution of equations of fourth and third orders
/ 150 \\
Use of Taylor's series for the boundary conditions /
156 \\
Additional notes and, bibliography / 158 \\
7. Eigenvalue Problems \\
Introduction / 159 \\
Properties of latent roots and vectors of matrices /
160 \\
Determination of latent roots and vectors of matrices /
162 \\
Relaxation / 163 \\
Example / 164 \\
Production of a second solution / 165 \\
Other methods / 167 \\
Matrix iteration. Real roots / 167 \\
Matrix iteration. Complex roots / 168 \\
Acceleration devices / 168 \\
Examples / 169 \\
Determination of a second solution / 173 \\
Mathematical connexions / 176 \\
Interpretation of finite-difference solutions / 179 \\
Algebraic treatment of differential systems / 180 \\
Relaxation. Simple examples / 181 \\
General description of method / 189 \\
Harder examples / 191 \\
Non-homogeneous eigenvalue problem / 198 \\
Boundary condition at infinity / 200 \\
Mixed boundary conditions / 205 \\
A fourth-order equation / 206 \\
Determination of a second solution / 209 \\
More accurate finite-difference equations / 210 \\
Other methods for differential systems / 211 \\
Inverse differential operators. Examples / 212 \\
Finite-difference methods for inverse differential
operators / 213 \\
Determination of a second solution / 218 \\
Direct differential operators / 219 \\
Harder problems. Simultaneous equations / 222 \\
Additional notes and bibliography / 225 \\
8. Initial-Value Techniques for Boundary-Value Problems
\\
Introduction / 228 \\
Linear second-order equations. Specified boundary
values / 228 \\
Linear second-order equations. Other boundary
conditions / 230 \\
A more general method / 232 \\
Inclusion of difference corrections / 233 \\
Equations of third and fourth orders / 241 \\
Eigenvalue problems / 245 \\
The difference correction / 249 \\
Fourth-order eigenvalue problems / 250 \\
Non-linear equations / 253 \\
Simultaneous differential equations / 258 \\
Difficulties and inaccuracies / 262 \\
Matching in the middle / 265 \\
Connexion with matrix methods and pure mathematics /
266 \\
Additional notes and bibliography / 272 \\
9. Accuracy and Precision of Boundary-Value Methods \\
Introduction / 274 \\
Precision of solutions of algebraic equations / 274 \\
Relaxation and precision / 278 \\
Further examination of triangular decomposition of
matrices / 282 \\
Second-order equations / 283 \\
Fourth-order equations / 286 \\
Effect of the second boundary / 289 \\
Some inverse matrices / 290 \\
General comments on precision. Nearness of
eigensolutions / 297 \\
Simultaneous differential equations / 298 \\
Errors in the solution of linear equations / 300 \\
Effect of a small diagonal term of $U$ / 302 \\
Effects of the difference correction / 310 \\
Convergence of the iterative method / 313 \\
Error introduced by the difference correction / 321 \\
Eigenvalue problems / 324 \\
Non-linear equations / 324 \\
Additional notes and bibliography / 324 \\
10. Miscellaneous Methods and Comments \\
Simultaneous differential equations / 326 \\
Equations with discontinuous coefficients / 328 \\
The deferred approach to the limit / 332 \\
Equations with eigensolutions / 343 \\
The equation $y'' + f(x) y = g(x)$, with one boundary
at infinity / 347 \\
Case $g(x) = 0$, $f(\infty) = k^2$ / 347 \\
Case $g(x) = 0$, $f(\infty) = -k^2$ / 352 \\
Case $g(x) \neq 0$ / 357 \\
Tabulation of functions for large arguments / 367 \\
Non-linear eigenvalue problems / 359 \\
Semi-analytical methods / 361 \\
Collocation / 362 \\
Least squares / 362 \\
The method of Galerkin / 362 \\
Eigenvalue problems / 363 \\
General comments / 363 \\
Additional notes and bibliography / 363 \\
Index / 365",
}
@Article{Fox:1957:RPN,
author = "L. Fox",
title = "Recent Publications: {{\booktitle{Numerical
Integration of Differential Equations}}, A. E. Bennett,
W. E. Milne, H. Bateman, Dover, New York, 1956, 108
pp.}",
journal = j-AMER-MATH-MONTHLY,
volume = "64",
number = "7",
pages = "520--520",
month = aug # "\slash " # sep,
year = "1957",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2308486",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "99-04",
MRnumber = "1529688",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/amermathmonthly1955.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Fox:1958:RPN,
author = "L. Fox",
title = "Recent Publications:{{\booktitle{Numerical Analysis}},
by Kaiser S. Kunz, McGraw-Hill, New York, 1957. xv +
381 pp.}",
journal = j-AMER-MATH-MONTHLY,
volume = "65",
number = "6",
pages = "464--465",
month = jun # "\slash " # jul,
year = "1958",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2310751",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "99-04",
MRnumber = "1530011",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/amermathmonthly1955.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Book{Fox:1958:TEI,
author = "L. Fox",
title = "Tables of {Everett} interpolation coefficients",
publisher = pub-HMSO,
address = pub-HMSO:adr,
pages = "61",
year = "1958",
bibdate = "Tue Nov 14 08:09:40 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
xxauthor = "L. Fox and J. D. Everett",
}
@InCollection{Fox:1959:MMT,
author = "L. Fox",
title = "Minimax methods in table construction",
crossref = "Langer:1959:NAP",
pages = "233--244",
year = "1959",
bibdate = "Tue Nov 14 08:12:46 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Fox:1959:SUD,
author = "L. Fox",
title = "Scientific uses of digital computers",
journal = "Bulletin of the Institute of Physics and the Physical
Society",
volume = "??",
number = "??",
pages = "185--188",
month = "????",
year = "1959",
bibdate = "Tue Nov 14 08:13:53 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "Bull. Inst. Phys.",
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Bulletin of the Institute of Physics and the Physical
Society",
}
@Article{Fox:1960:CAC,
author = "L. Fox",
title = "Checking in automatic computation",
journal = "Inst. Elec. Eng. and British Computer Society",
volume = "??",
number = "??",
pages = "14--16",
month = "????",
year = "1960",
bibdate = "Tue Nov 14 08:15:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@InCollection{Fox:1960:SNE,
author = "L. Fox",
editor = "R. E. Langer",
booktitle = "Boundary Problems in Differential Equations",
title = "Some numerical experiments with eigenvalue problems in
ordinary differential equations",
publisher = "The University of Wisconsin Press",
address = "Madison, WI, USA",
pages = "243--255",
year = "1960",
MRclass = "65.00",
MRnumber = "114302",
MRreviewer = "P. Henrici",
bibdate = "Tue Nov 14 08:17:32 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Fox:1960:TWP,
author = "L. Fox",
title = "Tables of {Weber} Parabolic Cylinder Functions and
Other Functions for Large Arguments",
volume = "4",
publisher = pub-HMSO,
address = pub-HMSO:adr,
pages = "iii + 40",
year = "1960",
MRclass = "65.00 (33.00)",
MRnumber = "120778",
MRreviewer = "L. J. Slater",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
note = "Department of Scientific and Industrial Research",
series = "National Physical Laboratory Mathematical Tables",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Cohen:1961:SCE,
author = "M. Cohen and C. A. Coulson",
title = "Single-centre expansions for the hydrogen molecular
ion",
journal = j-MATH-PROC-CAMB-PHILOS-SOC,
volume = "57",
number = "1",
pages = "96--106",
month = jan,
year = "1961",
CODEN = "PCPSA4",
DOI = "https://doi.org/10.1017/S0305004100034903",
ISSN = "0008-1981",
ISSN-L = "0305-0041",
bibdate = "Tue Nov 14 08:15:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
note = "Appendix by L. Fox",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Mathematical Proceedings of the Cambridge
Philosophical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP",
}
@Article{Fox:1961:BRF,
author = "L. Fox",
title = "Book Review: {{\booktitle{Finite Difference Methods
for Partial Differential Equations}}, by G. E. Forsythe
and W. R. Wasow, 1960; 444 pages. (London: John Wiley
\& Sons Ltd.; New York: John Wiley \& Sons)}",
journal = j-COMP-J,
volume = "4",
number = "1",
pages = "78--79",
month = jan,
year = "1961",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/4.1.78",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:26 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/4/1.toc;
https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/compj1960.bib",
note = "From the first paragraph: ``This is the first serious
book, in the era of automatic digital computing
machines, which is devoted solely to partial
differential equations and which treats all three major
types. Its publication is therefore a major event,
particularly at this state of intense development in
the numerical analysis of partial differential
equations.''",
URL = "http://comjnl.oxfordjournals.org/content/4/1/78.full.pdf+html",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Fox:1961:CMT,
author = "L. Fox",
title = "Computing Machines for Teaching and Research",
journal = j-COMP-J,
volume = "4",
number = "3",
pages = "212--216",
month = oct,
year = "1961",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/4.3.212",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "68.00",
MRnumber = "129097",
bibdate = "Tue Dec 4 14:47:27 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/4/3.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/compj.bib;
https://www.math.utah.edu/pub/tex/bib/compj1960.bib",
URL = "http://comjnl.oxfordjournals.org/content/4/3/212.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/040212.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/212.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/213.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/214.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/215.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/216.tif",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Fox:1961:SCA,
author = "L. Fox",
title = "Some comments on the accuracy and convenience of
finite-difference processes in scientific computation",
journal = "Proc. Ass. France de Calcul",
volume = "??",
number = "??",
pages = "63--73",
month = "????",
year = "1961",
bibdate = "Tue Nov 14 08:15:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Fox:1962:CMO,
author = "L. Fox",
title = "{Chebyshev} methods for ordinary differential
equations",
journal = j-COMP-J,
volume = "4",
number = "4",
pages = "318--331",
month = jan,
year = "1962",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/4.4.318",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65.61",
MRnumber = "136521",
MRreviewer = "D. Elliott",
bibdate = "Tue Dec 4 14:47:27 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/4/4.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_04/;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/compj.bib;
https://www.math.utah.edu/pub/tex/bib/compj1960.bib",
URL = "http://comjnl.oxfordjournals.org/content/4/4/318.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_04/040318.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_04/tiff/318.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_04/tiff/319.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_04/tiff/320.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_04/tiff/321.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_04/tiff/322.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_04/tiff/323.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_04/tiff/324.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_04/tiff/325.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_04/tiff/326.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_04/tiff/327.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_04/tiff/328.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_04/tiff/329.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_04/tiff/330.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_04/tiff/331.tif",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@InCollection{Fox:1962:MCA,
author = "L. Fox and H. F. Rainsford",
editor = "D. Clark",
booktitle = "Plane and geodetic surveying",
title = "Mechanical Computing. {Appendix I}",
publisher = "Constable",
address = "????",
pages = "615--634",
year = "1962",
bibdate = "Tue Nov 14 08:31:11 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Fox:1963:C,
author = "L. Fox and Andrew Young",
title = "Correspondence",
journal = j-COMP-J,
volume = "5",
number = "4",
pages = "296--296",
month = apr,
year = "1963",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/5.4.296",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:29 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/5/4.toc;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/compj1960.bib",
URL = "http://comjnl.oxfordjournals.org/content/5/4/296.full.pdf+html",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Fox:1963:PDE,
author = "L. Fox",
title = "Partial differential equations",
journal = j-COMP-J,
volume = "6",
number = "1",
pages = "69--74",
month = apr,
year = "1963",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/6.1.69",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65.65",
MRnumber = "155443",
bibdate = "Tue Dec 4 14:47:29 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/6/1.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/compj.bib;
https://www.math.utah.edu/pub/tex/bib/compj1960.bib",
URL = "http://comjnl.oxfordjournals.org/content/6/1/69.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/060069.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/69.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/70.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/71.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/72.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/73.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/74.tif",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Baker:1964:NSF,
author = "C. T. H. Baker and L. Fox and D. F. Mayers and K.
Wright",
title = "Numerical solution of {Fredholm} integral equations of
first kind",
journal = j-COMP-J,
volume = "7",
number = "2",
pages = "141--148",
month = jul,
year = "1964",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/7.2.141",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65.75",
MRnumber = "181126",
MRreviewer = "D. Elliott",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "http://comjnl.oxfordjournals.org/content/7/2.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_07/Issue_02/;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/compj.bib;
https://www.math.utah.edu/pub/tex/bib/compj1960.bib",
URL = "http://comjnl.oxfordjournals.org/content/7/2/141.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_07/Issue_02/070141.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_07/Issue_02/tiff/141.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_07/Issue_02/tiff/142.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_07/Issue_02/tiff/143.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_07/Issue_02/tiff/144.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_07/Issue_02/tiff/145.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_07/Issue_02/tiff/146.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_07/Issue_02/tiff/147.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_07/Issue_02/tiff/148.tif",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Book{Fox:1964:INL,
author = "L. Fox",
title = "An Introduction to Numerical Linear Algebra",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "xi + 295",
year = "1964",
LCCN = "QA251 .F65",
MRclass = "65.35",
MRnumber = "164436",
MRreviewer = "A. S. Householder",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
note = "Reprinted in 1967.",
series = "Monographs on Numerical Analysis",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
mynote = "Reprinted with corrections William Clowes, 1973.",
xxpages = "viii + 328",
}
@InCollection{Fox:1965:CLS,
author = "L. Fox",
editor = "D. C. Handscomb",
booktitle = "Approximation [Computing Laboratory Summer School]",
title = "{Chebyshev} least squares approximation",
chapter = "5",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "??--??",
year = "1965",
bibdate = "Tue Nov 14 08:36:55 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@InCollection{Fox:1965:DPC,
author = "L. Fox",
editor = "D. C. Handscomb",
booktitle = "Approximation [Computing Laboratory Summer School]",
title = "Determination and properties of {Chebyshev}
expansions",
chapter = "6",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "??--??",
year = "1965",
bibdate = "Tue Nov 14 08:36:55 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Fox:1965:INL,
author = "L. Fox",
title = "An Introduction to Numerical Linear Algebra, with
Exercises",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xi + 327",
year = "1965",
LCCN = "QA251 .F65 1965",
bibdate = "Tue Nov 14 06:56:10 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
series = "Monographs on Numerical Analysis",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
tableofcontents = "Introduction \\
Matrix algebra \\
Elimination methods of Gauss, Jordan and Aitken \\
Compact elimination methods of Doolittle, Crout,
Banachiewicz and Cholesky \\
Orthogonalisation methods \\
Condition, accuracy and precision \\
Comparison of methods. Measure of work \\
Iterative and gradient methods \\
Iterative methods for latent roots and vectors \\
Transformation methods for latent roots and vectors \\
Notes on error analysis for latent roots and vectors",
}
@InCollection{Fox:1965:LSA,
author = "L. Fox",
editor = "D. C. Handscomb",
booktitle = "Approximation [Computing Laboratory Summer School]",
title = "Least squares approximation, orthogonal polynomials",
chapter = "4",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "??--??",
year = "1965",
bibdate = "Tue Nov 14 08:36:55 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@InProceedings{Fox:1965:NMA,
author = "L. Fox",
editor = "????",
booktitle = "Proceedings of the International Symposium,
{Southampton}",
title = "Numerical methods for arch dams",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "169--187",
year = "1965",
bibdate = "Tue Nov 14 08:34:03 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Fox:1965:PAP,
author = "L. Fox",
title = "{Presidential Address}: The proper use of recurrence
relations",
journal = j-MATH-GAZ,
volume = "49",
number = "370",
pages = "371--387",
month = dec,
year = "1965",
CODEN = "MAGAAS",
DOI = "https://doi.org/10.2307/3612171",
ISSN = "0025-5572 (print), 2056-6328 (electronic)",
ISSN-L = "0025-5572",
bibdate = "Tue Nov 14 08:15:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
URL = "https://www.jstor.org/stable/3612171",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Mathematical Gazette",
journal-URL = "http://www.jstor.org/journal/mathgaze",
}
@InProceedings{Fox:1966:FCU,
author = "L. Fox and J. E. Walsh",
title = "Further comments on {University} work",
crossref = "Walsh:1966:NAI",
chapter = "12",
pages = "??--??",
year = "1966",
bibdate = "Tue Nov 14 08:45:10 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@InProceedings{Fox:1966:GS,
author = "L. Fox",
title = "General Survey",
crossref = "Walsh:1966:NAI",
chapter = "1",
pages = "??--??",
year = "1966",
bibdate = "Tue Nov 14 08:45:10 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Fox:1967:ABE,
author = "L. Fox and P. Henrici and C. B. Moler",
title = "Approximations and Bounds for Eigenvalues of Elliptic
Operators",
journal = j-SIAM-J-NUMER-ANAL,
volume = "4",
number = "1",
pages = "89--102",
month = mar,
year = "1967",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0704008",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65.66",
MRnumber = "0215542",
MRreviewer = "L. Collatz",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
JSTOR database",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992); Peter
Karl Henrici (13 September 1923--13 March 1987)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Fox:1967:RIC,
author = "L. Fox",
title = "{Romberg} integration for a class of singular
integrands",
journal = j-COMP-J,
volume = "10",
number = "1",
pages = "87--93",
month = may,
year = "1967",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/10.1.87",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65.55",
MRnumber = "213013",
MRreviewer = "Frank Stenger",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "http://comjnl.oxfordjournals.org/content/10/1.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_10/Issue_01/;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/compj.bib;
https://www.math.utah.edu/pub/tex/bib/compj1960.bib",
URL = "http://comjnl.oxfordjournals.org/content/10/1/87.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_10/Issue_01/100087.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_10/Issue_01/tiff/87.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_10/Issue_01/tiff/88.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_10/Issue_01/tiff/89.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_10/Issue_01/tiff/90.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_10/Issue_01/tiff/91.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_10/Issue_01/tiff/92.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_10/Issue_01/tiff/93.tif",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Fox:1968:BRP,
author = "L. Fox",
title = "Book Review: {{\booktitle{Proc{\'e}dures Algol en
Analyse Num{\'e}rique}}, 324 pages. (Published by Min.
de l'{\'E}ducation Nationale)}",
journal = j-COMP-J,
volume = "11",
number = "1",
pages = "30--30",
month = jan,
year = "1968",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/11.1.30",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:40 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/11/1.toc;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/compj1960.bib",
URL = "http://comjnl.oxfordjournals.org/content/11/1/30.full.pdf+html",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
remark-1 = "From the first paragraph: ``There are seven chapters,
with titles Linear Algebraic Equations (13 procedures),
Algebraic Eigenvalue Problem (17), Algebraic and
Non-linear Systems (11), Differential Systems, Integral
and Integro-differential Equations (6), Definite
Integrals (10), Approximation (13), Probability and
Special Functions (8).''",
remark-2 = "From the final paragraph: ``Extreme accuracy, of
course, is a necessity for a work of this kind, and the
stated checks and methods of producing the printed
pages give confidence that this has been achieved. This
is undoubtedly an important and practically useful
publication, and the team responsible for it deserve
our congratulations and thanks for a good idea
splendidly carried out.''",
}
@Book{Fox:1968:CMS,
author = "L. Fox and D. F. Mayers",
title = "Computing Methods for Scientists and Engineers",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "xii + 255",
year = "1968",
MRclass = "65.00",
MRnumber = "239715",
MRreviewer = "T. E. Hull",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
series = "Monographs on Numerical Analysis",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
mynote = "Quite a lot of error analysis, but all JHW stuff ---
nothing original. Good for the time, but nothing of
note.",
series-editor = "E. T. (Eric Thomson) Goodwin and D. R. Hartree and
Leslie Fox",
shorttableofcontents = "1: Problem formulation and choice of method /
1 \\
2: Error analysis and floating-point arithmetic / 15
\\
3: Computations with recurrence relations / 29 \\
4: Computations with polynomials / 55 \\
5: Computation with matrices / 75 \\
6: Polynomial approximation / 122 \\
7: Chebyshev approximation / 129 \\
8: Interpolation and differentiation. Finite
differences and Lagrangian methods / 145 \\
9: Numerical integration / 169 \\
10: Ordinary differential equations / 193 \\
Bibliography / 249 \\
Index / 251",
tableofcontents = "1. Problem Formulation and Choice of Method \\
Introduction / 1 \\
Formulation / 2 \\
Example 1 / 3 \\
Example 2 / 4 \\
Example 3 / 5 \\
Choice of method / 4 \\
The programme library / 6 \\
New programmes / 8 \\
Exercises 1 / 12 \\
\\
2. Error Analysis and Floating-Point Arithmetic \\
Introduction / 15 \\
Forward error analysis / 16 \\
Backward error analysis / 17 \\
Floating-point arithmetic / 19 \\
Addition and subtraction / 20 \\
Multiplication and division / 22 \\
Extended additions and multiplications / 23 \\
More accurate floating-point arithmetic / 25 \\
Exercises 2 / 27 \\
\\
3. Computations with Recurrence Relations \\
Introduction / 29 \\
First-order equations. Conditioning / 30 \\
Effect on problem formulation / 31 \\
Forward error analysis / 33 \\
Second-order equations. Initial-value problem / 36 \\
The homogeneous case. Ill-conditioning and problem
formulation / 36 \\
Non-homogeneous case / 39 \\
Forward error analysis / 40 \\
Second-order equations, boundary-value problem. A
stable method / 42 \\
An unstable method and its analysis / 44 \\
Ill-conditioned boundary-value problems / 48 \\
Problem reformulation: infinite range / 49 \\
Floating-point analysis / 50 \\
Exercises 3 / 52 \\
4. Computations with Polynomials \\
Introduction / 55 \\
Evaluation of polynomials. Error analysis / 55 \\
Zeros of polynomials. Ill-conditioning and problem
formulation / 59 \\
Computation of zeros / 62 \\
Accuracy of computed zeros / 64 \\
Computational comments / 67 \\
Deflation. Induced instability / 68 \\
Exercises 4 / 71 \\
\\
5. Computation with Matrices \\
Introduction / 75 \\
I. Linear equations / 75 \\
Ill-conditioning. Physical problem / 75 \\
Ill-conditioning. Mathematical problem / 78 \\
Induced instability / 80 \\
Elimination. Backward error analysis / 81 \\
Pivoting and stability / 85 \\
Compact method, fl, arithmetic / 86 \\
Completing the solution / 88 \\
Special cases / 88 \\
Accuracy and correction of solution / 91 \\
The inverse and the determinant / 95 \\
Iterative methods / 96 \\
II. The eigenvalue problem / 98 \\
Ill-conditioning / 99 \\
Stable methods, similarity transforms / 100 \\
Completing the solution / 103 \\
Induced instabilities / 106 \\
(i) Transformation methods / 106 \\
(ii) Vectors of transformed matrices / 108 \\
(iii) Matrix deflation / 111 \\
Iterative methods / 112 \\
Accuracy and correction of solution / 114 \\
III. The least-squares problem / 116 \\
Conclusion / 119 \\
Exercises 5 / 119 \\
\\
6. Polynomial Approximation \\
Introduction / 122 \\
Best approximation / 122 \\
The exchange algorithm / 123 \\
Good approximation / 124 \\
Power series / 125 \\
Interpolation / 126 \\
Exercises 6 / 127 \\
\\
7. Chebyshev Approximation \\
Introduction / 129 \\
The Chebyshev polynomial / 129 \\
Economization of power series / 131 \\
Interpolation / 133 \\
The Chebyshev series / 134 \\
Discrete ordinates / 136 \\
Rational functions / 137 \\
Differential equations / 140 \\
Exercises 7 / 143 \\
\\
8. Interpolation and Differentiation. Finite
Differences and Lagrangian Methods \\
Introduction / 145 \\
Lagrangian methods / 146 \\
(i) Interpolation / 146 \\
Neville's automatic interpolation / 148 \\
(ii) Inverse interpolation / 151 \\
(iii) Numerical differentiation / 152 \\
Finite-difference methods / 154 \\
(i) Difference tables / 154 \\
(ii) Direct interpolation / 159 \\
(iii) Inverse interpolation / 163 \\
(iv) Differentiation / 165 \\
Conclusion / 166 \\
Exercises 8 / 167 \\
\\
9. Numerical Integration \\
Introduction / 169 \\
Finite-difference methods / 170 \\
Lagrangian formulae, equal intervals / 174 \\
The deferred approach to the limit. Romberg integration
/ 176 \\
Lagrangian formulae, unequal intervals / 181 \\
Special cases / 182 \\
Singularities / 183 \\
Conclusion / 189 \\
Exercises 9 / 190 \\
\\
10. Ordinary Differential Equations \\
Introduction / 193 \\
Inherent instability / 194 \\
I. Initial-value problems / 197 \\
Methods that use derivatives / 198 \\
Methods that use finite differences / 199 \\
Lagrangian methods / 201 \\
(i) Truncated Taylor's series. Runge--Kutta methods /
201 \\
(ii) Truncated finite-difference methods. Special and
general predictor-corrector methods. / 202 \\
Treatment of the truncation error / 204 \\
(i) Local treatment / 205 \\
(ii) Global treatment. Deferred correction and other
Lagrangian methods / 206 \\
(iii) Different intervals and the deferred approach to
the limit / 210 \\
Induced instabilities / 212 \\
(i) Induced partial instability / 213 \\
(ii) Induced strong and weak instabilities / 216 \\
(iii) The non-linear case / 218 \\
II. Boundary-value and eigenvalue problems / 220 \\
Linear problems / 220 \\
Non-linear problems / 221 \\
Truncation error. Instabilities. Computational comments
/ 222 \\
Eigenvalue problems / 224 \\
III. Summary and examples / 227 \\
Example 1. Partial instability, finite-difference
method / 228 \\
Example 2. Partial instability, Runge--Kutta method /
229 \\
Example 8. Strong instability / 231 \\
Example 4. Weak instability / 232 \\
Example 5. Non-linear boundary-value problem, boundary-
value method / 232 \\
Example 6. Non-linear boundary-value problem,
initial-value method / 238 \\
Example 7. Eigenvalue problem, infinite range / 240 \\
Exercises 10 / 245 \\
\\
Bibliography / 249 \\
\\
Index / 251",
}
@Book{Fox:1968:CPN,
author = "L. Fox and I. B. Parker",
title = "{Chebyshev} Polynomials in Numerical Analysis",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "ix + 205",
year = "1968",
ISBN = "0-19-859614-6",
ISBN-13 = "978-0-19-859614-1",
LCCN = "QA297 .F65",
MRclass = "65.10",
MRnumber = "228149",
MRreviewer = "G. N. Lance",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
z3950.loc.gov:7090/Voyager",
note = "Reprinted in 1972 with corrections, but same ISBN.",
series = "Oxford mathematical handbooks",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
mynote = "JRUL: 517",
series-editor = "John Crank and C. C. Ritchie",
subject = "Chebyshev polynomials; Numerical analysis",
tableofcontents = "TO DO: find this!",
xxauthor = "L. (Leslie) Fox and I. B. (Ian Bax) Parker",
}
@Article{Fox:1968:CSN,
author = "L. Fox",
title = "Comments on singularities in numerical integration and
the solution of differential equations",
journal = "Colloquia Math Soc. Janos Bolyai",
volume = "??",
number = "??",
pages = "61--91",
year = "1968",
bibdate = "Tue Nov 14 08:15:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
note = "3 - Numerical Methods, Tihany, Hungary",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
remark = "TO DO: is this a journal, book, or conference
proceedings??",
}
@Article{Fox:1968:PFQ,
author = "L. Fox and Linda Hayes",
title = "Polynomial factorization and the {Q--D} algorithm",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "1",
number = "3",
pages = "445--463",
month = jul,
year = "1968",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(68)90019-0",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65.50",
MRnumber = "234626",
MRreviewer = "E. R. Hansen",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/linala1960.bib",
note = "See analysis \cite{Kershaw:1987:AMF}.",
URL = "http://www.sciencedirect.com/science/article/pii/0024379568900190",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@Article{Fox:1969:BSL,
author = "L. Fox and R. Sankar",
title = "Boundary singularities in linear elliptic differential
equations",
journal = j-J-INST-MATH-APPL,
volume = "5",
number = "3",
pages = "340--350",
month = sep,
year = "1969",
CODEN = "JMTAA8",
DOI = "https://doi.org/10.1093/imamat/5.3.340",
ISSN = "0020-2932",
ISSN-L = "0020-2932",
MRclass = "65.66",
MRnumber = "42 #1354 (266448)",
MRreviewer = "J. H. Bramble",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/jinstmathappl.bib",
URL = "https://academic.oup.com/imamat/article/5/3/340/697349",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Journal of the Institute of Mathematics and its
Applications",
journal-URL = "http://imamat.oxfordjournals.org/content/by/year",
}
@Article{Fox:1969:CEM,
author = "L. Fox",
title = "Computer Evaluation of Mathematical Function",
journal = j-COMP-J,
volume = "12",
number = "3",
pages = "267--267",
month = aug,
year = "1969",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/12.3.267",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:43 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/12/3.toc;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/compj1960.bib",
URL = "http://comjnl.oxfordjournals.org/content/12/3/267.full.pdf+html",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@InCollection{Fox:1969:MPP,
author = "L. Fox",
title = "Mathematical and physical polynomials",
crossref = "Dejon:1969:CAF",
pages = "63--68",
year = "1969",
bibdate = "Tue Nov 14 08:52:33 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Nichols:1969:GCO,
author = "Nancy K. Nichols and L. Fox",
title = "Generalized consistent ordering and the optimum
successive over-relaxation factor",
journal = j-NUM-MATH,
volume = "13",
number = "5",
pages = "425--433",
month = oct,
year = "1969",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02163270",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.35",
MRnumber = "258261",
MRreviewer = "T. A. Porsching",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Fox:1970:DIS,
author = "L. Fox and Linda Hayes",
title = "On the Definite Integration of Singular Integrands",
journal = j-SIAM-REVIEW,
volume = "12",
number = "3",
pages = "449--457",
month = jul,
year = "1970",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1012084",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65.55",
MRnumber = "270557",
MRreviewer = "Alan M. Cohen",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "http://epubs.siam.org/toc/siread/12/3;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "SIAM Review. A Publication of the Society for
Industrial and Applied Mathematics",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "July 1970",
}
@InCollection{Fox:1970:I,
author = "L. Fox",
editor = "J. G. Hayes",
booktitle = "Numerical Approximation to Functions and Data",
title = "Introduction",
chapter = "1",
publisher = "IMA and Athlone Press, London University",
address = "London, UK",
pages = "??",
year = "1970",
bibdate = "Tue Nov 14 09:02:27 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Fox:1970:MCM,
author = "L. Fox and E. T. Goodwin and J. G. L. Michel and F. W.
J. Olver and J. H. Wilkinson",
title = "Modern Computing Methods",
volume = "16",
publisher = pub-HMSO,
address = pub-HMSO:adr,
edition = "Second",
pages = "vii + 169",
year = "1970",
ISBN = "0-11-480021-9",
ISBN-13 = "978-0-11-480021-5",
LCCN = "QA297 .T4 1970",
bibdate = "Wed Nov 15 11:52:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
series = "NPL Notes on Applied Science",
acknowledgement = ack-nhfb,
author-dates = "Frank William John Olver (15 December 1924--23 April
2013); James H. Wilkinson (27 September 1919--5 October
1986); Leslie Fox (30 September 1918--1 August 1992)",
subject = "Numerical analysis; Equations; Numerical solutions;
Computers; Analyse num{\'e}rique; {\'E}quations;
Solutions num{\'y}eriques; Ordinateurs",
tableofcontents = "TO DO: find this!",
}
@Article{Fox:1971:FDE,
author = "L. Fox and D. F. Mayers and J. R. Ockendon and A. B.
Tayler",
title = "On a functional differential equation",
journal = j-J-INST-MATH-APPL,
volume = "8",
number = "3",
pages = "271--307",
month = dec,
year = "1971",
CODEN = "JMTAA8",
DOI = "https://doi.org/10.1093/imamat/8.3.271",
ISSN = "0020-2932",
ISSN-L = "0020-2932",
MRclass = "34K99 (65Q05)",
MRnumber = "46 #488 (301330)",
MRreviewer = "K. Zima",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/jinstmathappl.bib",
ZMnumber = "0251.34045",
abstract = "See printed version",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
classmath = "*34K05 General theory of functional-differential
equations 34E05 Asymptotic expansions (ODE) 34E10
Asymptotic perturbations (ODE) 65L05 Initial value
problems for ODE (numerical methods)",
fjournal = "Journal of the Institute of Mathematics and its
Applications",
journal-URL = "http://imamat.oxfordjournals.org/content/by/year",
}
@Article{Fox:1971:HGM,
author = "L. Fox",
title = "How to Get Meaningless Answers in Scientific
Computation (and What to Do About It)",
journal = j-IMA-BULL,
volume = "7",
number = "10",
pages = "296--302",
year = "1971",
bibdate = "Wed Feb 15 21:40:25 GMT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "IMA Bulletin",
}
@Article{Fox:1971:SES,
author = "L. Fox",
title = "Some experiments with singularities in linear elliptic
partial differential equations",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "323",
number = "1553",
pages = "179--190",
month = jun,
year = "1971",
CODEN = "PRLAAZ",
DOI = "https://doi.org/10.1098/rspa.1971.0095",
ISSN = "0962-8444 (print), 2053-9177 (electronic)",
ISSN-L = "0962-8444",
MRclass = "65N15",
MRnumber = "494991",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical, Physical and Engineering Sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/",
}
@Article{Young:1971:BRC,
author = "A. Young and L. Fox and D. F. Mayers",
title = "Book reviews: {{\booktitle{Convexity and Optimization
in Finite Dimensions I}}, by Josef Stoer and Christoph
Witzgall, 1970; \booktitle{On Round-off Errors in
Linear Programming}, by H. M{\"u}ller-Merbach, 1970;
\booktitle{Approximation Theory}, edited by A. Talbot,
1970}",
journal = j-COMP-J,
volume = "14",
number = "4",
pages = "390--390",
month = nov,
year = "1971",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/14.4.390",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Oct 03 06:35:05 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/compj.bib;
https://www.math.utah.edu/pub/tex/bib/compj1970.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/tiff/390.tif",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Fox:1972:TNA,
author = "L. Fox",
title = "The teaching of numerical analysis",
journal = j-BULL-INST-MATH-APPL,
volume = "8",
number = "??",
pages = "255--258",
month = "????",
year = "1972",
CODEN = "IMTABW",
ISSN = "0950-5628",
ISSN-L = "0950-5628",
bibdate = "Tue Nov 14 08:15:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Bulletin of the Institute of Mathematics and its
Applications",
}
@InCollection{Fox:1973:DEP,
author = "L. Fox and Linda Hayes and D. F. Mayers",
editor = "J. J. H. Miller",
booktitle = "Topics in numerical analysis ({Proceedings of the
Royal Irish Academy Conference, University College,
Dublin, 1972})",
title = "The double eigenvalue problem",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "93--112",
year = "1973",
MRclass = "65L15",
MRnumber = "345423",
MRreviewer = "K. Najzar",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
remark = "Published for the Royal Irish Academy by Academic
Press.",
}
@Book{Fox:1973:INL,
author = "L. Fox",
title = "An Introduction to Numerical Linear Algebra",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "xi + 328",
year = "1973",
ISBN = "0-19-853402-7 (hardcover), 0-19-853407-8 (paperback)",
ISBN-13 = "978-0-19-853402-0 (hardcover), 978-0-19-853407-5
(paperback)",
LCCN = "QA251 .F65",
bibdate = "Tue Nov 14 07:02:11 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
note = "Reprinted in \cite{Fox:1979:INL}.",
series = "Monographs on Numerical Analysis",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
series-editor = "E. T. (Eric Thomson) Goodwin and D. R. Hartree and
Leslie Fox",
tableofcontents = "TO DO: find this!",
}
@Article{Fox:1973:RFM,
author = "L. Fox and R. Sankar",
title = "The {Regula-Falsi} method for free-boundary problems",
journal = j-J-INST-MATH-APPL,
volume = "12",
number = "1",
pages = "49--54",
month = aug,
year = "1973",
CODEN = "JMTAA8",
DOI = "https://doi.org/10.1093/imamat/12.1.49",
ISSN = "0020-2932",
ISSN-L = "0020-2932",
bibdate = "Sat Apr 6 16:15:03 MST 2002",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/jinstmathappl.bib",
ZMnumber = "0262.65072",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Journal of the Institute of Mathematics and its
Applications",
journal-URL = "http://imamat.oxfordjournals.org/content/by/year",
}
@Article{Fox:1973:RNM,
author = "B. L. Fox",
title = "Reducing the Number of Multiplikations in Iterative
Processes",
journal = j-ACTA-INFO,
volume = "3",
number = "1",
pages = "43--45",
day = "31",
month = dec,
year = "1973",
CODEN = "AINFA2",
ISSN = "0001-5903 (print), 1432-0525 (electronic)",
ISSN-L = "0001-5903",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Misc/HBP/ACTAI.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/actainfo.bib",
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Acta Informatica",
journal-URL = "http://link.springer.com/journal/236",
}
@Article{Fox:1974:BRI,
author = "L. Fox",
title = "Book Review: {{\booktitle{Introduction to Matrix
Computations}}, G. W. Stewart, 1973; 441 pages
(Academic Press)}",
journal = j-COMP-J,
volume = "17",
number = "3",
pages = "200--200",
month = mar,
year = "1974",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/17.3.200",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:54 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/17/3.toc;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
https://www.math.utah.edu/pub/tex/bib/compj1970.bib",
URL = "http://comjnl.oxfordjournals.org/content/17/3/200.full.pdf+html",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Fox:1974:CLC,
author = "L. Fox and Linda Hayes",
title = "Computation of the lemniscate constants",
journal = j-BULL-INST-MATH-APPL,
volume = "10",
number = "??",
pages = "425--426",
month = "????",
year = "1974",
CODEN = "IMTABW",
ISSN = "0950-5628",
ISSN-L = "0950-5628",
bibdate = "Tue Nov 14 08:15:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Bulletin of the Institute of Mathematics and its
Applications",
xxnote = "Check author order",
}
@Article{Fox:1974:TFB,
author = "L. Fox",
title = "Two free-boundary problems with singularities",
journal = "Acta Universitatis Carolinae. Mathematica et Physica",
volume = "15",
number = "1--2",
pages = "19--23",
year = "1974",
ISSN = "0001-7140",
ISSN-L = "0001-7140",
MRclass = "65N99",
MRnumber = "386305",
MRreviewer = "I. Norman Katz",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "Acta Univ. Carolin. Math. Phys.",
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Acta Universitatis Carolinae. Mathematica et Physica",
}
@InCollection{Fox:1975:F,
author = "L. Fox and J. H. Wilkinson",
booktitle = "The {NAG} Library Manual",
title = "Foreward",
publisher = pub-NAG,
address = pub-NAG:adr,
pages = "1--3",
year = "1975",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Fox:1975:FH,
author = "L. Fox and Linda Hayes",
title = "A further helping of $ \pi $",
journal = j-MATH-GAZ,
volume = "59",
number = "407",
pages = "38--40",
month = mar,
year = "1975",
CODEN = "MAGAAS",
DOI = "https://doi.org/10.2307/3616808",
ISSN = "0025-5572 (print), 2056-6328 (electronic)",
ISSN-L = "0025-5572",
bibdate = "Tue Nov 14 08:15:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib",
URL = "https://www.jstor.org/stable/3616808",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Mathematical Gazette",
journal-URL = "http://www.jstor.org/journal/mathgaze",
remark = "Comment on Richardson's extrapolation methods for
computing $ \pi $ from successive inscribed polygons,
and report that ``The results are rather spectacular,
the two correct figures in $ p_{24} $ giving rise, with
a relatively trivial amount of extra arithmetic, to
nine correct figures in $ p'''_{24} $. Convergence
acceleration of this kind is obviously especially
valuable when computation of successive values of $ p_n
$, as here, is not trivial and is increasingly
contaminated with rounding errors.''",
}
@InCollection{Fox:1975:INA,
author = "L. Fox",
editor = "B. L. Hewitt and others",
booktitle = "Computational methods and problems in aeronautical
fluid dynamics: {Proceedings of IMA Conference, 1974}",
title = "Introductory Numerical Analysis",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "15--52",
year = "1975",
bibdate = "Tue Nov 14 09:17:21 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@InCollection{Fox:1975:WBN,
author = "L. Fox",
editor = "J. R. Ockendon and W. R. Hodgkins",
booktitle = "Moving Boundary Problems in Heat flow and Diffusion",
title = "What are the best numerical methods?",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "210--241",
year = "1975",
bibdate = "Tue Nov 14 09:13:43 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Fox:1976:BRC,
author = "L. Fox",
title = "Book Review: {{\booktitle{The Chebyshev Polynomials}},
Theodore J. Rivlin, 1974; 186 pages (John Wiley)}",
journal = j-COMP-J,
volume = "19",
number = "1",
pages = "42--42",
month = jan,
year = "1976",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/19.1.42",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:57 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/19/1.toc;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/compj1970.bib",
URL = "http://comjnl.oxfordjournals.org/content/19/1/42.full.pdf+html",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Fox:1976:NAC,
author = "L. Fox",
title = "Numerical analysis, computers and problem solving",
journal = "Interdisciplinary Science Reviews",
volume = "1",
number = "2",
pages = "167--175",
month = "????",
year = "1976",
CODEN = "ISCRD8",
DOI = "https://doi.org/10.1179/isr.1976.1.2.167",
ISSN = "0308-0188 (print), 1743-2790 (electronic)",
ISSN-L = "0308-0188",
bibdate = "Tue Nov 14 08:15:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "Interdisciplinary Sc. Rev.",
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Interdisciplinary Science Reviews",
}
@InProceedings{Fox:1977:FDM,
author = "L. Fox",
title = "Finite-difference methods for elliptic boundary-value
problems",
crossref = "Jacobs:1977:SAN",
chapter = "7",
pages = "799--881",
year = "1977",
MRclass = "65N10 (65N20)",
MRnumber = "474863",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
xxtitle = "Finite difference methods for elliptic boundary value
problems",
}
@Article{Fox:1977:IEP,
author = "L. Fox",
title = "An inverse eigenvalue problem",
journal = j-BULL-INST-MATH-APPL,
volume = "13",
number = "6",
pages = "162--163",
month = "????",
year = "1977",
CODEN = "IMTABW",
ISSN = "0905-5628",
MRclass = "65L15",
MRnumber = "440934",
MRreviewer = "C. W. Gear",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "Bull. Inst. Math. Appl.",
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Bulletin of the Institute of Mathematics and its
Applications",
}
@InProceedings{Fox:1978:AAJ,
author = "L. Fox",
booktitle = "The Contribution of {Dr. J. H. Wilkinson} to Numerical
Analysis",
title = "All About {Jim Wilkinson}, with a Commemorative
Snippet on Backward Error Analysis",
volume = "19",
publisher = inst-IMA-UK,
address = inst-IMA-UK:adr,
pages = "1--20",
year = "1978",
bibdate = "Mon Nov 21 22:18:58 GMT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
series = "Symposium Proceedings Series",
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@InCollection{Fox:1979:FDS,
author = "L. Fox",
editor = "I. Gladwell and R. Wait",
booktitle = "A Survey of Numerical Methods for Partial Differential
Equations",
title = "Finite differences and singularities in elliptic
problems",
chapter = "3",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "42--79",
year = "1979",
bibdate = "Tue Nov 14 09:36:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Fox:1979:INL,
author = "L. Fox",
title = "An Introduction to Numerical Linear Algebra",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "xi + 328",
year = "1979",
ISBN = "0-19-853402-7, 0-19-853407-8",
ISBN-13 = "978-0-19-853402-0, 978-0-19-853407-5",
LCCN = "QA251 .F65",
bibdate = "Tue Nov 14 07:02:11 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
note = "Reprint of \cite{Fox:1973:INL}.",
series = "Monographs on Numerical Analysis",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
tableofcontents = "TO DO: find this!",
}
@InCollection{Fox:1979:SP,
author = "L. Fox",
editor = "I. Gladwell and R. Wait",
booktitle = "A Survey of Numerical Methods for Partial Differential
Equations",
title = "The {Stefan} problem",
chapter = "??",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "332--356",
year = "1979",
bibdate = "Tue Nov 14 09:36:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@InCollection{Fox:1980:NMB,
author = "L. Fox",
editor = "I. Gladwell and D. K. Sayers",
booktitle = "Computational techniques for ordinary differential
equations ({Proceedings of the Conference University of
Manchester, Manchester, 1978})",
title = "Numerical methods for boundary value problems",
chapter = "9",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "175--216",
year = "1980",
ISBN = "0-12-285780-1",
ISBN-13 = "978-0-12-285780-5",
MRclass = "65L10",
MRnumber = "582978",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
series = "Inst. Math. Appl. Conf. Ser.",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Fox:1980:SEI,
author = "L. Fox and M. R. Valenca",
title = "Some experiments with interval methods for two-point
boundary value problems in ordinary differential
equations",
journal = j-BIT,
volume = "20",
number = "1",
pages = "67--82",
month = mar,
year = "1980",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933587",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65L10 (65G10)",
MRnumber = "81f:65059 (569978)",
MRreviewer = "E. R. Hansen",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "file://sunblast.math.utah.edu/home/0077/sy/beebe/tex/bib/bit.bib;
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=20&issue=1;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=20&issue=1&spage=67",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "BIT. Nordisk Tidskrift for Informationsbehandling
(BIT)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "Interval arithmetic",
}
@Article{Fox:1981:FDM,
author = "L. Fox",
title = "Finite-difference methods for elliptic boundary value
problems",
journal = "Yingyong Shuxue yu Jisuan Shuxue",
number = "3",
pages = "11--34",
year = "1981",
MRclass = "65N10 (65N20)",
MRnumber = "656305",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
note = "Translated from the English by Xue Zong Liu and Lie
Heng Wang",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Yingyong Shuxue yu Jisuan Shuxue. Applied Mathematics
and Computational Mathematics",
}
@Article{Fox:1981:NSI,
author = "L. Fox and D. F. Mayers",
title = "On the numerical solution of implicit ordinary
differential equations",
journal = j-IMA-J-NUMER-ANAL,
volume = "1",
number = "4",
pages = "377--401",
month = oct,
year = "1981",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/1.4.377",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65L05",
MRnumber = "83a:65061 (641317)",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Fox:1983:CSL,
author = "L. Fox",
title = "Computers still have a lot to learn about good
numerical analysis and numerical algorithms",
journal = j-NAG-NEWSLETTER,
volume = "2",
number = "??",
pages = "5--15",
month = "????",
year = "1983",
ISSN = "0269-0780",
ISSN-L = "0269-0780",
bibdate = "Tue Nov 14 08:15:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "NAG Newsletter",
}
@Article{Fox:1984:NAH,
author = "L. Fox",
title = "Numerical analysis in higher education",
journal = j-BULL-INST-MATH-APPL,
volume = "20",
number = "??",
pages = "103--108",
month = "????",
year = "1984",
CODEN = "IMTABW",
ISSN = "0950-5628",
ISSN-L = "0950-5628",
bibdate = "Tue Nov 14 08:15:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
note = "Presented at the Symposium on ``The contribution of
Leslie Fox to numerical analysis''.",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Bulletin of the Institute of Mathematics and its
Applications",
}
@Misc{Fox:1985:BNA,
author = "L. Fox",
title = "The beginnings of numerical analysis",
howpublished = "Lecture to British Society for the History of
Mathematics, King's College, London",
year = "1985",
bibdate = "Tue Nov 14 09:51:08 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@InProceedings{Fox:1985:CAM,
author = "L. Fox",
editor = "????",
booktitle = "Proceedings of the {Tenth Canadian Congress of Applied
Mechanics, University of Western Ontario}",
title = "Chairman's address: Mathematical and numerical
modelling",
publisher = "????",
address = "????",
pages = "1--10",
year = "1985",
bibdate = "Tue Nov 14 09:49:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@InProceedings{Fox:1987:ENA,
author = "L. Fox",
title = "Early numerical analysis in the {United Kingdom}",
crossref = "Crane:1987:HAC",
pages = "21--39",
year = "1987",
DOI = "https://doi.org/10.1145/41579.41581",
bibdate = "Tue Nov 14 14:18:12 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
remark = "Typescript: see \cite{Fox:1990:ENA} for typeset
version.",
}
@Article{Fox:1987:JHW,
author = "L. Fox",
title = "{James Hardy Wilkinson, 27 September 1919--5 October
1986}",
journal = j-BIOGRAPH-MEMOIRS-FELLOWS-ROY-SOC,
volume = "33",
pages = "669--708",
month = dec,
year = "1987",
CODEN = "BMFRA3",
DOI = "https://doi.org/10.1098/rsbm.1987.0024",
ISSN = "0080-4606 (print), 1748-8494 (electronic)",
ISSN-L = "0080-4606",
bibdate = "Wed Aug 23 08:44:07 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/biograph-memoirs-fellows-roy-soc.bib",
URL = "http://www.jstor.org/stable/7699a67;
https://royalsocietypublishing.org/doi/epdf/10.1098/rsbm.1987.0024",
acknowledgement = ack-nhfb,
ajournal = "Biogr. Mem. Fell. R. Soc. Lond.",
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "Biographical Memoirs of Fellows of the Royal Society",
journal-URL = "http://www.jstor.org/journals/00804606.html;
https://royalsocietypublishing.org/loi/rsbm;
https://www.jstor.org/journal/biogmemofellroya;
https://royalsocietypublishing.org/journal/rsbm",
published = "01 December 1987",
}
@Book{Fox:1987:NSO,
author = "L. Fox and D. F. Mayers",
title = "Numerical Solution of Ordinary Differential
Equations",
publisher = pub-CHAPMAN-HALL,
address = pub-CHAPMAN-HALL:adr,
pages = "xii + 249",
year = "1987",
DOI = "https://doi.org/10.1007/978-94-009-3129-9",
ISBN = "0-412-22650-2",
ISBN-13 = "978-0-412-22650-2",
LCCN = "QA372 .F69 1987",
MRclass = "65-01 (65Lxx)",
MRnumber = "936630",
MRreviewer = "G. K. Gupta",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
shorttableofcontents = "1: Introduction / 1 \\
2: Sensitivity analysis: inherent instability / 14 \\
3: Initial-value problems: one-step methods / 42 \\
4: Initial-value problems: multi-step methods / 78 \\
5: Initial-value methods for boundary-value problems /
98 \\
6: Global (finite-difference) methods for
boundary-value problems / 128 \\
7: Expansion methods / 179 \\
8: Algorithms / 198 \\
9: Further notes and bibliography / 212 \\
10: Answers to selected exercises / 231 \\
11: Index / 247",
tableofcontents = "Preface / ix \\
1 Introduction / 1 \\
1.1 Differential equations and associated conditions /
1 \\
1.2 Linear and non-linear differential equations / 4
\\
1.3 Uniqueness of solutions / 6 \\
1.4 Mathematical and numerical methods of solution / 7
\\
1.5 Difference equations / 9 \\
1.6 Additional notes / 11 \\
Exercises / 12 \\
\\
2 Sensitivity analysis: inherent instability / 14 \\
2.1 Introduction / 14 \\
2.2 A simple example of sensitivity analysis / 16 \\
2.3 Variational equations / 18 \\
2.4 Inherent instability of linear recurrence
relations. Initial-value problems / 20 \\
2.5 Inherent instability of linear differential
equations. Initial-value problems / 27 \\
2.6 Inherent instability: boundary-value problems / 29
\\
2.7 Additional notes / 33 \\
Exercises / 39 \\
\\
3 Initial-value problems: one-step methods / 42 \\
3.1 Introduction / 42 \\
3.2 Three possible one-step methods (finite-difference
methods) / 43 \\
3.3 Error analysis: linear problems / 44 \\
3.4 Error analysis and techniques for non-linear
problems / 48 \\
3.5 Induced instability: partial instability / 51 \\
3.6 Systems of equations / 56 \\
3.7 Improving the accuracy / 58 \\
3.8 More accurate one-step methods / 62 \\
3.9 Additional notes / 69 \\
Exercises / 75 \\
\\
4 Initial-value problems: multi-step methods / 78 \\
4.1 Introduction / 78 \\
4.2 Multi-step finite-difference formulae / 78 \\
4.3 Convergence, consistency and zero stability / 80
\\
4.4 Partial and other stabilities / 83 \\
4.5 Predictor--corrector methods / 88 \\
4.6 Error estimation and choice of interval / 90 \\
4.7 Starting the computation / 91 \\
4.8 Changing the interval / 92 \\
4.9 Additional notes / 94 \\
Exercises / 95 \\
\\
5 Initial-value methods for boundary-value problems /
98 \\
5.1 Introduction / 98 \\
5.2 The shooting method: linear problems / 99 \\
5.3 The shooting method: non-linear problems / 101 \\
54 The shooting method: eigenvalue problems / 103 \\
5.5 The shooting method: problems with unknown
boundaries / 106 \\
5.6 Induced instabilities of shooting methods / 108 \\
5.7 Avoiding induced instabilities / 113 \\
5.8 Invariant embedding for linear problems / 117 \\
5.9 Additional notes / 121 \\
Exercises / 125 \\
\\
6 Global (finite-difference) methods for boundary-value
problems / 128 \\
6.1 Introduction / 128 \\
6.2 Solving linear algebraic equations / 129 \\
6.3 Linear differential equations of orders two and
four / 135 \\
6.4 Simultaneous linear differential equations of first
order / 141 \\
6.5 Convenience and accuracy of methods / 143 \\
6.6 Improvement of accuracy / 144 \\
6.7 Non-linear problems / 154 \\
6.8 Continuation for non-linear problems / 157 \\
6.9 Additional notes / 160 \\
Exercises / 174 \\
\\
7 Expansion methods / 179 \\
7.1 Introduction / 179 \\
7.2 Properties and computational importance of
Chebyshev polynomials / 179 \\
7.3 Chebyshev solution of ordinary differential
equations/ 181 \\
7.4 Spline solution of boundary-value problems / 189
\\
7.5 Additional notes / 192 \\
Exercises/ 195 \\
\\
8 Algorithms / 198 \\
8.1 Introduction / 198 \\
8.2 Routines for initial-value problems / 199 \\
8.3 Routines for boundary-value problems / 207 \\
\\
9 Further notes and bibliography / 212 \\
\\
10 Answers to selected exercises / 231 \\
\\
Index / 247",
}
@Article{Fox:1987:ODJ,
author = "Leslie Fox",
title = "Obituary: {Dr. J. H. Wilkinson, F.R.S.}",
journal = j-COMP-J,
volume = "30",
number = "1",
pages = "1--1",
year = "1987",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/30.1.1",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "01A70",
MRnumber = "88e:01054",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_30/Issue_01/;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/compj.bib;
https://www.math.utah.edu/pub/tex/bib/compj1980.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_30/Issue_01/tiff/1.tif",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
remark = "Article lost at publisher Web site, and DOI and URL no
longer resolve.",
}
@InProceedings{Fox:1990:EJW,
author = "L. Fox",
title = "Epilogue. {Jim Wilkinson}: {Some} After-Dinner
Sentiments",
crossref = "Cox:1990:RNC",
pages = "329--335",
year = "1990",
MRclass = "01A70",
MRnumber = "1098333",
bibdate = "Tue Nov 2 19:30:33 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
series = "Oxford Sci. Publ.",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
mycrossref = "Cox:1990:RNC",
}
@InCollection{Fox:1990:ENA,
author = "L. Fox",
title = "Early numerical analysis in the {United Kingdom}",
crossref = "Nash:1990:HSC",
pages = "280--300",
year = "1990",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
remark-1 = "From page 294: ``About this time there were other
small groups in other government and government-type
laboratories, and at several universities, particularly
Cambridge and Manchester, who were also working on
computer construction and use. Comrie had formed the
London Scientific Computing Service, which Miller
joined, but as far as the mathematics of numerical
analysis was concerned the NPL group was by far the
largest and the most experienced. There is no doubt
that what you would call the more modern numerical
analysis in the UK started with this group which,
indeed, was dominant in our numerical work for at least
30 years.''",
remark-2 = "From page 295: ``In the middle nineteen-fifties and
onwards there was a flood of books and papers on
numerical analysis of all kinds and from many places,
largely stimulated by the development of the
stored-program computer. The NPL contribution to this
feast was supplied very largely by J. H. Wilkinson. His
third relevant paper (1955) [\cite{Wilkinson:1955:UIM}]
was merely the first of a series which for the next
thirty years transformed both the theory and the
practice of virtually all problems in numerical linear
algebra.''",
}
@Book{Fox:1990:NST,
author = "L. Fox",
title = "The Numerical Solution of Two-point Boundary Problems
in Ordinary Differential Equations",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xii + 371",
year = "1990",
ISBN = "0-486-66495-3",
ISBN-13 = "978-0-486-66495-8",
MRclass = "65-01 (65L10)",
MRnumber = "1088251",
bibdate = "Mon Nov 13 14:02:18 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
note = "Reprint of \cite{Fox:1957:NST}.",
series = "Monographs on Numerical Analysis",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
series-editor = "E. T. (Eric Thomson) Goodwin and D. R. Hartree and
Leslie Fox",
shorttableofcontents = "1. Introduction / 2 \\
2. Finite Differences and Finite-Difference / 6 \\
3. The Solution of Algebraic Equations / 34 \\
4. Second-Order Equations / 67 \\
5. First-Order Equations / 106 \\
6. Equations of Higher Orders / 128 \\
7. Eigenvalue Problems 159 / 159 \\
8. Initial-Value Techniques For Boundary-Value Problems
/ 228 \\
9. Accuracy and Precision of Boundary-Value Methods /
274 \\
10. Miscellaneous Methods and Comments / 326 \\
Index / 365",
tableofcontents = "1. Introduction \\
Definitions / 1 \\
Analytical and numerical solutions / 2 \\
Boundary conditions and initial conditions / 3 \\
Additional notes and bibliography / 5 \\
2, Finite Differences and Finite-Difference Equations
\\
Introduction / 6 \\
Differences / 6 \\
Operators / 7 \\
Interpolation 9 / 17 \\
Differentiation / 10 \\
Integration / 12 \\
Sums and sum operators / 13 \\
Relations between formulae / 17 \\
The difference correction / 17 \\
Tables of formulae / 18 \\
The practical application of finite-difference
equations / 20 \\
Convergent differences / 22 \\
Numerical applications. Accuracy and precision / 24 \\
Divergent differences / 27 \\
Recapitulation / 30 \\
Lagrangian formulae / 31 \\
Additional notes and bibliography / 32 \\
3. The Solution of Algebraic Equations \\
Differential equations and algebraic equations / 34 \\
The difference correction / 35 \\
Linear algebraic equations. Iterative methods / 36 \\
The relaxation method / 36 \\
Notes on relaxation / 39 \\
Condition and convergence / 42 \\
Direct methods / 45 \\
Non-linear equations / 47 \\
Solution of simultaneous finite-difference equations /
49 \\
Relaxation: a computational arrangement for difference
equations / 50 \\
Relaxation: second-order equations / 51 \\
Relaxation: simultaneous second-order equations / 56
\\
Relaxation: fourth-order equations / 57 \\
Relaxation: equations of odd order / 58 \\
Direct methods: second-order equations / 59 \\
Direct methods: simultaneous second-order equations /
61 \\
Direct methods: fourth-order equations / 62 \\
Direct methods: equations of odd order / 63 \\
General comments / 64 \\
Additional notes and bibliography / 67 \\
4. Second-Order Equations \\
Introduction / 67 \\
Finite-difference equations / 67 \\
Simple examples: boundary values specified / 68 \\
Boundary condition involving derivative. Simple example
/ 74 \\
An alternative to the difference correction. Iteration
/ 79 \\
Example / 80 \\
Simultaneous second-order equations / 81 \\
Non-linear equations / 84 \\
Iterative methods. Examples / 86 \\
The `$\eta$ method / 87 \\
Boundary condition at infinity / 91 \\
Mixed boundary conditions / 93 \\
Change of interval / 94 \\
Singularities / 98 \\
The use of Taylor's series for boundary conditions /
101 \\
Additional notes and bibliography / 103 \\
5. First-Order Equations \\
Introduction / 106 \\
Finite-difference equations and boundary conditions /
106 \\
Compatibility of boundary values. Simple examples / 107
\\
A practical example / 111 \\
A smaller difference correction 113 Alternative methods
/ 113 \\
Method 1 / 114 \\
Method 2 / 116 \\
Method 3 / 117 \\
Solution of the linear equations / 117 \\
Normalization / 118 \\
Transformation to second-order differential equation /
119 \\
Choice of method. Illustrative example / 122 \\
Additional notes and bibliography / 125 \\
6. Equations of Higher Orders \\
Fourth-order linear equations / 128 \\
General boundary conditions / 128 \\
Special boundary conditions / 130 \\
Method of solution. Simple example / 131 \\
Other methods of solution / 134 \\
Other boundary conditions / 137 \\
Third-order equations / 138 \\
Oscillation. / 138 \\
Example / 138 \\
Discussion of oscillation / 140 \\
Removal of oscillation / 141 \\
Example / 143 \\
Transformation to second-order equation / 144 \\
Example / 145 \\
Other transformations / 148 \\
Equations of order higher than the fourth, Non-linear
equations / 150 \\
Matrix solution of equations of fourth and third orders
/ 150 \\
Use of Taylor's series for the boundary conditions /
156 \\
Additional notes and, bibliography / 158 \\
7. Eigenvalue Problems \\
Introduction / 159 \\
Properties of latent roots and vectors of matrices /
160 \\
Determination of latent roots and vectors of matrices /
162 \\
Relaxation / 163 \\
Example / 164 \\
Production of a second solution / 165 \\
Other methods / 167 \\
Matrix iteration. Real roots / 167 \\
Matrix iteration. Complex roots / 168 \\
Acceleration devices / 168 \\
Examples / 169 \\
Determination of a second solution / 173 \\
Mathematical connexions / 176 \\
Interpretation of finite-difference solutions / 179 \\
Algebraic treatment of differential systems / 180 \\
Relaxation. Simple examples / 181 \\
General description of method / 189 \\
Harder examples / 191 \\
Non-homogeneous eigenvalue problem / 198 \\
Boundary condition at infinity / 200 \\
Mixed boundary conditions / 205 \\
A fourth-order equation / 206 \\
Determination of a second solution / 209 \\
More accurate finite-difference equations / 210 \\
Other methods for differential systems / 211 \\
Inverse differential operators. Examples / 212 \\
Finite-difference methods for inverse differential
operators / 213 \\
Determination of a second solution / 218 \\
Direct differential operators / 219 \\
Harder problems. Simultaneous equations / 222 \\
Additional notes and bibliography / 225 \\
8. Initial-Value Techniques for Boundary-Value Problems
\\
Introduction / 228 \\
Linear second-order equations. Specified boundary
values / 228 \\
Linear second-order equations. Other boundary
conditions / 230 \\
A more general method / 232 \\
Inclusion of difference corrections / 233 \\
Equations of third and fourth orders / 241 \\
Eigenvalue problems / 245 \\
The difference correction / 249 \\
Fourth-order eigenvalue problems / 250 \\
Non-linear equations / 253 \\
Simultaneous differential equations / 258 \\
Difficulties and inaccuracies / 262 \\
Matching in the middle / 265 \\
Connexion with matrix methods and pure mathematics /
266 \\
Additional notes and bibliography / 272 \\
9. Accuracy and Precision of Boundary-Value Methods \\
Introduction / 274 \\
Precision of solutions of algebraic equations / 274 \\
Relaxation and precision / 278 \\
Further examination of triangular decomposition of
matrices / 282 \\
Second-order equations / 283 \\
Fourth-order equations / 286 \\
Effect of the second boundary / 289 \\
Some inverse matrices / 290 \\
General comments on precision. Nearness of
eigensolutions / 297 \\
Simultaneous differential equations / 298 \\
Errors in the solution of linear equations / 300 \\
Effect of a small diagonal term of $U$ / 302 \\
Effects of the difference correction / 310 \\
Convergence of the iterative method / 313 \\
Error introduced by the difference correction / 321 \\
Eigenvalue problems / 324 \\
Non-linear equations / 324 \\
Additional notes and bibliography / 324 \\
10. Miscellaneous Methods and Comments \\
Simultaneous differential equations / 326 \\
Equations with discontinuous coefficients / 328 \\
The deferred approach to the limit / 332 \\
Equations with eigensolutions / 343 \\
The equation $y'' + f(x) y = g(x)$, with one boundary
at infinity / 347 \\
Case $g(x) = 0$, $f(\infty) = k^2$ / 347 \\
Case $g(x) = 0$, $f(\infty) = -k^2$ / 352 \\
Case $g(x) \neq 0$ / 357 \\
Tabulation of functions for large arguments / 367 \\
Non-linear eigenvalue problems / 359 \\
Semi-analytical methods / 361 \\
Collocation / 362 \\
Least squares / 362 \\
The method of Galerkin / 362 \\
Eigenvalue problems / 363 \\
General comments / 363 \\
Additional notes and bibliography / 363 \\
Index / 365",
}
@InCollection{Fox:1993:NA,
author = "L. Fox",
editor = "P. G. Drazin",
booktitle = "Collected papers of {Lewis Fry Richardson}",
title = "Numerical Analysis",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "??--??",
year = "1993",
bibdate = "Tue Nov 14 09:52:20 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
note = "This is Leslie Fox's final publication.",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Bartlett:1952:IPH,
author = "James H. Bartlett",
title = "Iterative procedures and the helium wave equation",
journal = j-PHYS-REV-2,
volume = "88",
number = "3",
pages = "525--526",
month = nov,
year = "1952",
CODEN = "PHRVAO",
DOI = "https://doi.org/10.1103/PhysRev.88.525",
ISSN = "0031-899X (print), 1536-6065 (electronic)",
ISSN-L = "0031-899X",
MRclass = "65.0X",
MRnumber = "52208",
MRreviewer = "L. Fox",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
abstract = "In an attempt to solve the helium wave equation
exactly, study of a 180-point mesh shows the need for
an improved difference operator to approximate the
Laplacian. Such an operator has been developed,
allowing one to express the value of the function at
one point in terms of the values at 26 neighboring
points (in three dimensions)",
fjournal = "Physical Review. Series II",
journal-URL = "http://journals.aps.org/archive/browse",
received = "16 July 1952",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Fischbach:1953:NSN,
author = "Joseph W. Fischbach",
title = "The Numerical Solution of Non-linear Differential
Equations by the Method of Steepest Descent",
publisher = "Ballistic Research Laboratories",
address = "Aberdeen Proving Ground, MD, USA",
pages = "23",
year = "1953",
MRclass = "65.0X",
MRnumber = "78050",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
note = "Memo. Rep. No. 646",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Milne:1953:NSD,
author = "William Edmund Milne",
title = "Numerical Solution of Differential Equations",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xii + 275",
year = "1953",
MRclass = "65.0X",
MRnumber = "68321",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Southwell:1953:SEP,
author = "R. V. Southwell and Gillian Vaisey",
title = "On some eigenvalue problems of exceptional difficulty,
exemplified by a case of elastic instability",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "6",
number = "4",
pages = "453--480",
year = "1953",
CODEN = "QJMMAV",
DOI = "https://doi.org/10.1093/qjmam/6.4.453",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
MRclass = "65.0X",
MRnumber = "59637",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "The Quarterly Journal of Mechanics and Applied
Mathematics",
journal-URL = "http://qjmam.oxfordjournals.org/content/by/year",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Spencer:1953:CPA,
author = "L. V. Spencer",
title = "Calculation of peaked angular distributions from
{Legendre} polynomial expansions and an application to
the multiple scattering of charged particles",
journal = j-PHYS-REV-2,
volume = "90",
number = "1",
pages = "146--150",
month = apr,
year = "1953",
CODEN = "PHRVAO",
DOI = "https://doi.org/10.1103/PhysRev.90.146",
ISSN = "0031-899X (print), 1536-6065 (electronic)",
ISSN-L = "0031-899X",
MRclass = "65.0X",
MRnumber = "54347",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Physical Review. Series II",
journal-URL = "http://journals.aps.org/archive/browse",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Sterne:1953:ANS,
author = "Theodore E. Sterne",
title = "The accuracy of numerical solutions of ordinary
differential equations",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "7",
number = "43",
pages = "159--164",
month = jul,
year = "1953",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1953-0057627-8",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "65.0X",
MRnumber = "57627",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Allen:1954:RM,
author = "D. N. de G. Allen",
title = "Relaxation Methods",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "ix + 257",
year = "1954",
MRclass = "65.0X",
MRnumber = "61468",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Blanc:1954:FIA,
author = "Charles Blanc",
title = "Sur les formules d'int{\'e}gration approch{\'e}e
d'{\'e}quations diff{\'e}rentielles. ({French}) [{On}
the formulas for approximate integration of
differential equations]",
journal = j-ARCH-MATH,
volume = "5",
pages = "301--308",
year = "1954",
CODEN = "ACVMAL",
DOI = "https://doi.org/10.1007/BF01898369",
ISSN = "0003-889X (print), 1420-8938 (electronic)",
ISSN-L = "0003-889X",
MRclass = "65.0X",
MRnumber = "64488",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Archiv der Mathematik",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/13",
language = "French",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Reynolds:1954:TSC,
author = "George E. Reynolds",
title = "Table of Squares of Cosecants",
publisher = "Air Force Cambridge Research Center, Electronics
Research Directorate",
address = "Cambridge, MA, USA",
pages = "iv + 89",
year = "1954",
MRclass = "65.1X",
MRnumber = "74941",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Anonymous:1955:TDE,
author = "Anonymous",
title = "Table of the Descending Exponential, $ x = 2.5 $ to
$ x = 10 $",
volume = "46",
publisher = pub-USGPO,
address = pub-USGPO:adr,
pages = "v + 76",
year = "1955",
MRclass = "65.1X",
MRnumber = "74129",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
series = "National Bureau of Standards Applied Mathematics
Series",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Anonymous:1955:THS,
author = "Anonymous",
title = "Table of Hyperbolic Sines and Cosines, $ x = 2 $ to
$ x = 10 $",
volume = "45",
publisher = pub-USGPO,
address = pub-USGPO:adr,
pages = "v + 81",
year = "1955",
MRclass = "65.1X",
MRnumber = "74128",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
series = "National Bureau of Standards Applied Mathematics
Series",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Blanch:1955:TCV,
author = "Gertrude Blanch and Ida Rhodes",
title = "Table of characteristic values of {Mathieu}'s equation
for large values of the parameter",
journal = j-J-WASH-ACAD-SCI,
volume = "45",
number = "6",
pages = "166--196",
month = jun,
year = "1955",
CODEN = "JWASA3",
ISSN = "0043-0439",
ISSN-L = "0043-0439",
MRclass = "65.1X",
MRnumber = "71144",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
URL = "https://www.jstor.org/stable/24533649",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Washington Academy of Sciences",
journal-URL = "http://www.jstor.org/journal/jwashacadscie",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Booth:1955:NAP,
author = "A. D. Booth",
title = "A note on approximating polynomials for trigonometric
functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "9",
number = "49",
pages = "21--23",
month = jan,
year = "1955",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1955-0069579-7",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "65.0X",
MRnumber = "69579",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{deVogelaere:1955:MNI,
author = "Rene {de Vogelaere}",
title = "A method for the numerical integration of differential
equations of second order without explicit first
derivatives",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "54",
pages = "119--125",
year = "1955",
DOI = "https://doi.org/10.6028/jres.054.014",
ISSN = "0160-1741 (print), 2376-5259 (electronic)",
ISSN-L = "0160-1741",
MRclass = "65.0X",
MRnumber = "68910",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Research of the National Bureau of
Standards",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@TechReport{Householder:1955:GED,
author = "Alston S. Householder",
title = "The Generation of Error in Digital Computation",
type = "Technical Report",
number = "ORNL-1983",
institution = inst-ORNL,
address = inst-ORNL:adr,
pages = "iv + 79",
day = "11",
month = oct,
year = "1955",
DOI = "https://doi.org/10.2172/4380237",
MRclass = "68.0X",
MRnumber = "0073314",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/householder-alston-s.bib",
URL = "https://www.osti.gov/biblio/4380237-generation-error-digital-computation",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Kaye:1955:TFE,
author = "Joseph Kaye",
title = "A table of the first eleven repeated integrals of the
error function",
journal = j-J-MATH-PHYS,
volume = "34",
pages = "119--125",
year = "1955",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1002/sapm1955341119",
ISSN = "0097-1421",
ISSN-L = "0022-2488",
MRclass = "65.0X",
MRnumber = "69575",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematics and Physics",
journal-URL = "http://jmp.aip.org/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Rowe:1955:DAP,
author = "Paul P. Rowe",
title = "Difference approximations to partial derivatives for
uneven spacings in the network",
journal = "Transactions. American Geophysical Union",
volume = "36",
number = "6",
pages = "995--1008",
month = dec,
year = "1955",
CODEN = "TAGUAT",
DOI = "https://doi.org/10.1029/TR036i006p00995",
ISSN = "0002-8606 (print), 2379-6723 (electronic)",
ISSN-L = "0002-8606",
MRclass = "65.0X",
MRnumber = "77232",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "Trans. Amer. Geophys. Union",
fjournal = "Transactions. American Geophysical Union",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Rutishauser:1955:BNI,
author = "Heinz Rutishauser",
title = "{Bemerkungen zur numerischen Integration
gew{\"o}hnlicher Differentialgleichungen $n$-ter
Ordnung}. ({German}) [{Remarks} on the numerical
integration of ordinary differential equations $n$-th
order]",
journal = j-Z-ANGE-MATH-PHYS,
volume = "6",
number = "6",
pages = "497--498",
month = nov,
year = "1955",
CODEN = "ZAMPDB",
DOI = "https://doi.org/10.1007/BF01600536",
ISSN = "0044-2275 (print), 1420-9039 (electronic)",
ISSN-L = "0044-2275",
MRclass = "65.0X",
MRnumber = "74924",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib",
acknowledgement = ack-nhfb,
author-dates = "Heinz Rutishauser (30 January 1918--10 November
1970)",
fjournal = "Zeitschrift f{\"u}r Angewandte Mathematik und Physik.
ZAMP. Journal of Applied Mathematics and Physics.
Journal de Math{\'e}matiques et de Physique
Appliqu{\'e}es",
journal-URL = "http://link.springer.com/journal/33",
language = "German",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Salzer:1955:CZE,
author = "Herbert E. Salzer",
title = "Complex zeros of the error function",
journal = j-J-FRANKLIN-INST,
volume = "260",
number = "3",
pages = "209--211",
month = sep,
year = "1955",
CODEN = "JFINAB",
DOI = "https://doi.org/10.1016/0016-0032(55)90732-8",
ISSN = "0016-0032 (print), 1879-2693 (electronic)",
ISSN-L = "0016-0032",
MRclass = "65.1X",
MRnumber = "71880",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Franklin Institute",
journal-URL = "http://www.sciencedirect.com/science/journal/00160032",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Zaroodny:1955:ERM,
author = "S. J. Zaroodny",
title = "An Elementary Review of the {Mathieu--Hill} Equation
of Real Variable Based on Numerical Solutions",
publisher = "Ballistic Research Laboratories",
address = "Aberdeen Proving Ground, MD, USA",
pages = "29",
year = "1955",
MRclass = "65.1X",
MRnumber = "74944",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
note = "Memo. Rep. No. 878",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Blanc:1956:IAE,
author = "Charles Blanc",
title = "Sur l'int{\'e}gration approch{\'e}e d'{\'e}quations du
type parabolique. ({French}) [{On} the approximate
integration of parabolic type equations]",
journal = j-Z-ANGE-MATH-PHYS,
volume = "7",
number = "2",
pages = "146--152",
month = mar,
year = "1956",
CODEN = "ZAMPDB",
DOI = "https://doi.org/10.1007/BF01600784",
ISSN = "0044-2275 (print), 1420-9039 (electronic)",
ISSN-L = "0044-2275",
MRclass = "65.3X",
MRnumber = "81555",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Zeitschrift f{\"u}r Angewandte Mathematik und Physik.
ZAMP. Journal of Applied Mathematics and Physics.
Journal de Math{\'e}matiques et de Physique
Appliqu{\'e}es",
journal-URL = "http://link.springer.com/journal/33",
language = "French",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Buchdahl:1956:ATF,
author = "H. A. Buchdahl",
title = "{{\"U}ber Approximationen der Thomas--Fermi-Funktion}.
({German}) [{On} approximations of the {Thomas--Fermi}
function]",
journal = j-ANN-PHYS-6,
volume = "17",
pages = "238--241",
year = "1956",
CODEN = "ANPYA2",
DOI = "https://doi.org/10.1002/andp.19564520408",
ISSN = "0003-3804 (print), 1521-3889 (electronic)",
ISSN-L = "0003-3804",
MRclass = "65.0X",
MRnumber = "78049",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Ann. Physik (6)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-3889",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Chisnall:1956:MCE,
author = "G. A. Chisnall",
title = "A modified {Chebyshev--Everett} interpolation
formula",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "10",
number = "54",
pages = "66--73",
month = apr,
year = "1956",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1956-0081529-7",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "65.3X",
MRnumber = "81529",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Davis:1956:AWG,
author = "P. Davis and P. Rabinowitz",
title = "Abscissas and weights for {Gaussian} quadratures of
high order",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "56",
pages = "35--37",
year = "1956",
DOI = "https://doi.org/10.6028/jres.056.005",
ISSN = "0160-1741 (print), 2376-5259 (electronic)",
ISSN-L = "0160-1741",
MRclass = "65.1X",
MRnumber = "76463",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Research of the National Bureau of
Standards",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Hildebrand:1956:INA,
author = "F. B. Hildebrand",
title = "Introduction to Numerical Analysis",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "x + 511",
year = "1956",
MRclass = "65.0X",
MRnumber = "75670",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Horgan:1956:TCP,
author = "R. B. Horgan",
title = "Table of coefficients for the partial summation of
series",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "10",
number = "55",
pages = "156--162",
month = jul,
year = "1956",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1956-0084202-4",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "65.1X",
MRnumber = "84202",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Huckel:1956:TFW,
author = "Vera Huckel",
title = "Tabulation of the $ f_\lambda $ functions which occur
in the aerodynamic theory of oscillating wings in
supersonic flow",
journal = "NACA Technical Note",
volume = "1956",
number = "3606",
pages = "59",
year = "1956",
ISSN = "0097-2177",
ISSN-L = "0097-2177",
MRclass = "65.1X",
MRnumber = "78056",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "National Advisory Committee for Aeronautics. Technical
Note",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Jaeger:1956:NVT,
author = "J. C. Jaeger",
title = "Numerical values for the temperature in radial heat
flow",
journal = j-J-MATH-PHYS,
volume = "34",
pages = "316--321",
year = "1956",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1002/sapm1955341316",
ISSN = "0097-1421",
ISSN-L = "0022-2488",
MRclass = "65.1X",
MRnumber = "74945",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematics and Physics",
journal-URL = "http://jmp.aip.org/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Krarup:1956:MMM,
author = "T. Krarup and Bj. Svejgaard",
title = "A method for matrix multiplication, matrix inversion,
and problems of adjustment by punched card equipment",
journal = "Geod{\ae}tisk Institut, K{\o}benhavn. Meddelelser",
volume = "1956",
number = "31",
pages = "31",
year = "1956",
MRclass = "65.3X",
MRnumber = "80990",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Geodaet. Inst., K{\o}benhavn. Medd.",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Lipow:1956:RE,
author = "M. Lipow and S. A. Zwick",
title = "On the roots of the equation: {$ Y_1 (m x)[x J_1 (x) -
B J_0 (x)] - J \sb 1 (m x)[x Y_1 (x) - B Y_0 (x)] = 0.
$}",
journal = j-J-MATH-PHYS,
volume = "34",
pages = "308--315",
year = "1956",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1002/sapm1955341308",
ISSN = "0097-1421",
ISSN-L = "0022-2488",
MRclass = "65.1X",
MRnumber = "74943",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematics and Physics",
journal-URL = "http://jmp.aip.org/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Lotkin:1956:NSL,
author = "Mark Lotkin",
title = "Note on the sensitivity of least squares solutions",
journal = j-J-MATH-PHYS,
volume = "35",
pages = "309--311",
year = "1956",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1002/sapm1956351309",
ISSN = "0097-1421",
ISSN-L = "0022-2488",
MRclass = "65.3X",
MRnumber = "84854",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematics and Physics",
journal-URL = "http://jmp.aip.org/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Mendelsohn:1956:SEP,
author = "N. S. Mendelsohn",
title = "Some elementary properties of ill conditioned matrices
and linear equations",
journal = j-AMER-MATH-MONTHLY,
volume = "63",
number = "5",
pages = "285--295",
month = may,
year = "1956",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2310510",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "65.0X",
MRnumber = "78043",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
URL = "https://www.jstor.org/stable/2310510",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Robertson:1956:PCN,
author = "H. H. Robertson",
title = "Phase calculations for nuclear scattering on the
{Pilot ACE}",
journal = j-MATH-PROC-CAMB-PHILOS-SOC,
volume = "52",
number = "3",
pages = "538--545",
month = jun,
year = "1956",
CODEN = "MPCPCO",
DOI = "https://doi.org/10.1017/S0305004100031534",
ISSN = "0305-0041 (print), 1469-8064 (electronic)",
ISSN-L = "0305-0041",
MRclass = "68.0X",
MRnumber = "81567",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Proceedings of the Cambridge
Philosophical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Roth:1956:VMS,
author = "J. P. Roth and D. S. Scott",
title = "A vector method for solving linear equations and
inverting matrices",
journal = j-J-MATH-PHYS,
volume = "35",
pages = "312--317",
year = "1956",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1002/sapm1956351312",
ISSN = "0097-1421",
ISSN-L = "0022-2488",
MRclass = "65.3X",
MRnumber = "84858",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematics and Physics",
journal-URL = "http://jmp.aip.org/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Salzer:1956:FIO,
author = "Herbert E. Salzer",
title = "Formulas for inverse osculatory interpolation",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "56",
pages = "51--54",
year = "1956",
DOI = "https://doi.org/10.6028/jres.056.007",
ISSN = "0160-1741 (print), 2376-5259 (electronic)",
ISSN-L = "0160-1741",
MRclass = "65.0X",
MRnumber = "76431",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Research of the National Bureau of
Standards",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Salzer:1956:FPS,
author = "Herbert E. Salzer",
title = "Formulas for the partial summation of series",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "10",
number = "55",
pages = "149--156",
month = jul,
year = "1956",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1956-0081528-5",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "65.3X",
MRnumber = "81528",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Uchida:1956:RFB,
author = "Shigeo Uchida and Michiru Yasuhara",
title = "The rotational field behind a curved shock wave
calculated by the method of flux analysis",
journal = "Journal of the Aeronautical Sciences",
volume = "23",
number = "9",
pages = "830--854",
year = "1956",
CODEN = "JASCAR",
DOI = "https://doi.org/10.2514/8.3670",
ISSN = "0095-9812",
ISSN-L = "0095-9812",
MRclass = "76.0X",
MRnumber = "80489",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Aero. Sci.",
fjournal = "Journal of the Aeronautical Sciences",
journal-URL = "https://arc.aiaa.org/loi/jans",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Young:1956:REA,
author = "Robert L. Young",
title = "Report on experiments in approximating the solution of
a differential equation",
journal = j-J-ACM,
volume = "3",
number = "1",
pages = "26--28",
month = jan,
year = "1956",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/320815.320822",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65.0X",
MRnumber = "75683",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Altman:1957:SLA,
author = "M. Altman",
title = "On the solution of linear algebraic equations",
journal = j-BULL-ACAD-POL-SCI-CL-3,
volume = "5",
pages = "93--97, IX",
year = "1957",
CODEN = "BPSMA6",
ISSN = "0554-5897",
ISSN-L = "0554-5897",
MRclass = "65.3X",
MRnumber = "86377",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Bull. Acad. Polon. Sci. Cl. III.",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Clenshaw:1957:NSL,
author = "C. W. Clenshaw",
title = "The numerical solution of linear differential
equations in {Chebyshev} series",
journal = j-MATH-PROC-CAMB-PHILOS-SOC,
volume = "53",
number = "1",
pages = "134--149",
month = jan,
year = "1957",
CODEN = "MPCPCO",
DOI = "https://doi.org/10.1017/s0305004100032072",
ISSN = "0305-0041 (print), 1469-8064 (electronic)",
ISSN-L = "0305-0041",
MRclass = "65.3X",
MRnumber = "82196",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Charles William Clenshaw (15 March 1926--23 September
2004)",
fjournal = "Mathematical Proceedings of the Cambridge
Philosophical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Meyer:1957:MIL,
author = "H. I. Meyer and B. J. Hollingsworth",
title = "A method of inverting large matrices of special form",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "58",
pages = "94--97",
month = apr,
year = "1957",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1957-0086381-2",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "65.3X",
MRnumber = "86381",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Salzer:1957:NIU,
author = "Herbert E. Salzer",
title = "Numerical integration of $ y'' = \phi (x, y, y') $
using osculatory interpolation",
journal = j-J-FRANKLIN-INST,
volume = "263",
number = "5",
pages = "401--409",
month = may,
year = "1957",
CODEN = "JFINAB",
DOI = "https://doi.org/10.1016/0016-0032(57)90279-X",
ISSN = "0016-0032 (print), 1879-2693 (electronic)",
ISSN-L = "0016-0032",
MRclass = "65.3X",
MRnumber = "85608",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Franklin Institute",
journal-URL = "http://www.sciencedirect.com/science/journal/00160032",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Stegun:1957:GBF,
author = "Irene A. Stegun and Milton Abramowitz",
title = "Generation of {Bessel} functions on high speed
computers",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "60",
pages = "255--257",
month = oct,
year = "1957",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1957-0093939-3",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "68.00 (65.00)",
MRnumber = "93939",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Viswanathan:1957:SPE,
author = "R. V. Viswanathan",
title = "Solution of {Poisson}'s equation by relaxation
method---normal gradient specified on curved
boundaries",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "58",
pages = "67--78",
month = apr,
year = "1957",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1957-0086396-4",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "65.3X",
MRnumber = "86396",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Warner:1957:SJP,
author = "F. J. Warner",
title = "On the solution of ``jury'' problems with many degrees
of freedom",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "60",
pages = "268--271",
month = oct,
year = "1957",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1957-0094909-1",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "65.00",
MRnumber = "94909",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Bauer:1958:MMI,
author = "F. L. Bauer",
title = "On Modern Matrix Iteration Processes of {Bernoulli}
and {Graeffe} Type",
journal = j-J-ACM,
volume = "5",
number = "3",
pages = "246--257",
month = jul,
year = "1958",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/320932.320935",
ISSN = "0004-5411 (print), 1557-735x (electronic)",
ISSN-L = "0004-5411",
MRclass = "65.00",
MRnumber = "117876",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/jacm.bib",
ZMID = "03160601",
ZMnumber = "0098.31404",
acknowledgement = ack-nhfb,
author-dates = "Friedrich (``Fritz'') Ludwig Bauer (10 June 1924--26
March 2015)",
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "Bernoulli's method; Graeffe's method; nla; nlop;
polynomial",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Gauss:1958:FVL,
author = "F. G. Gauss",
title = "{F{\"u}nfstellige vollst{\"a}ndige logarithmische und
trigonometrische Tafeln. Herausgegeben von Dr.-Ing. H.
H. Gobbin}. ({German}) [{Five}-digit complete
logarithmic and trigonometric tables. {Published} by
{Dr.-Ing. H. H. Gobbin}]",
publisher = "Verlag Konrad Wittwer",
address = "Stuttgart, West Germany",
pages = "xxxii + 184",
year = "1958",
MRclass = "65.00",
MRnumber = "100971",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
note = "391.-400. Aufl",
acknowledgement = ack-nhfb,
language = "German",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Hersch:1958:ROS,
author = "Joseph Hersch",
title = "R{\'e}currences d'ordre sup{\'e}rieur pour des
{\'e}quations aux diff{\'e}rences. ({French})
[{Higher}-order repetitions for difference equations]",
journal = j-C-R-ACAD-SCI-PARIS,
volume = "246",
pages = "264--367",
year = "1958",
ISSN = "0001-4036 (print), 2419-6304 (electronic)",
ISSN-L = "0001-4036",
MRclass = "65.00",
MRnumber = "96364",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Comptes Rendus Hebdomadaires des S{\'e}ances de
l'Acad{\'e}mie des Sciences",
journal-URL = "http://gallica.bnf.fr/ark:/12148/cb343481087/date",
language = "French",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@InProceedings{Kuntzmann:1958:CFL,
author = "J. Kuntzmann",
booktitle = "Symposium on modern computers: {Proceedings of the
Rome Symposium (17--18 October 1956) organized by the
Preparatory Committee of the International Computation
Center under the auspices of UNESCO}",
title = "Calcul de fonctions de {Legendre}. ({French})
[{Calculation} of {Legendre} functions]",
publisher = "Veschi",
address = "Rome, Italy",
pages = "1--3",
year = "1958",
MRclass = "65.00",
MRnumber = "106554",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Rossiter:1958:ARM,
author = "J. R. Rossiter",
title = "On the application of relaxation methods to oceanic
tides",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "248",
number = "1255",
pages = "482--498",
month = dec,
year = "1958",
CODEN = "PRLAAZ",
DOI = "https://doi.org/10.1098/rspa.1958.0257",
ISSN = "0962-8444 (print), 2053-9177 (electronic)",
ISSN-L = "0962-8444",
MRclass = "86.00 (65.00)",
MRnumber = "99882",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical, Physical and Engineering Sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Salzer:1958:TBO,
author = "Herbert E. Salzer and Genevieve M. Kimbro",
title = "Tables for Bivariate Osculatory Interpolation over a
{Cartesian} Grid",
publisher = "Convair Division of General Dynamics Corporation",
address = "San Diego, CA, USA",
pages = "40",
year = "1958",
MRclass = "65.00",
MRnumber = "99106",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Salzer:1958:TIE,
author = "Herbert E. Salzer and Norman Levine",
title = "Table of integers not exceeding $ 1{\,}000{\,}000 $
that are not expressible as the sum of four tetrahedral
numbers",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "12",
number = "62",
pages = "141--144",
month = apr,
year = "1958",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1958-0099756-3",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "65.00",
MRnumber = "99756",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Wittmeyer:1958:NMD,
author = "H. Wittmeyer",
title = "A new method for developing simple formulae for the
eigenvalues of linear ordinary self-adjoint
differential equations",
journal = j-J-SIAM,
volume = "6",
number = "2",
pages = "111--143",
month = jun,
year = "1958",
CODEN = "JSIMAV",
DOI = "https://doi.org/10.1137/0106007",
ISSN = "0368-4245 (print), 2168-3484 (electronic)",
ISSN-L = "0368-4245",
MRclass = "65.00",
MRnumber = "93906",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Society for Industrial and Applied
Mathematics",
journal-URL = "http://epubs.siam.org/loi/smjmap.1",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Borwein:1959:EBC,
author = "David Borwein and Andrew R. Mitchell",
title = "The effect of boundary conditions and mesh size on the
accuracy of finite difference solutions of two-point
boundary problems",
journal = j-Z-ANGE-MATH-PHYS,
volume = "10",
number = "3",
pages = "221--232",
month = may,
year = "1959",
CODEN = "ZAMPDB",
DOI = "https://doi.org/10.1007/BF01600603",
ISSN = "0044-2275 (print), 1420-9039 (electronic)",
ISSN-L = "0044-2275",
MRclass = "65.00",
MRnumber = "106546",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Zeitschrift f{\"u}r Angewandte Mathematik und Physik.
ZAMP. Journal of Applied Mathematics and Physics.
Journal de Math{\'e}matiques et de Physique
Appliqu{\'e}es",
journal-URL = "http://link.springer.com/journal/33",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Chatelet:1959:TPC,
author = "F. Ch{\^a}telet and G. Lansraux and B. Million",
title = "Tables pour le calcul approch{\'e} des int{\'e}grales
finies de {Hankel}. ({French}) [{Tables} for the
approximate calculation of finite {Hankel} integrals]",
journal = j-CHIFFRES,
volume = "2",
pages = "233--237",
year = "1959",
ISSN = "0245-9922",
ISSN-L = "0245-9922",
MRclass = "62.00 (65.00)",
MRnumber = "109394",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Chiffres",
language = "French",
remark = "Journal has no online archives.",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Hof:1959:TPN,
author = "Hans Hof",
title = "Ten Place Natural Trigonometric Tables: Sine--Tangent,
$0$ to $ 90 $ Degrees",
publisher = "Professional Supply Company",
address = "Jenkintown, PA, USA",
pages = "iv + 1084",
year = "1959",
MRclass = "65.00",
MRnumber = "112265",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Jenson:1959:VFR,
author = "V. G. Jenson",
title = "Viscous flow round a sphere at low {Reynolds} numbers
$ ( < 40) $",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "249",
number = "1258",
pages = "346--366",
month = jan,
year = "1959",
CODEN = "PRLAAZ",
DOI = "https://doi.org/10.1098/rspa.1959.0029",
ISSN = "0962-8444 (print), 2053-9177 (electronic)",
ISSN-L = "0962-8444",
MRclass = "76.00",
MRnumber = "99819",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical, Physical and Engineering Sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@InProceedings{Miller:1959:EAS,
author = "J. C. P. Miller",
booktitle = "On numerical approximation. {Proceedings} of a
{Symposium}, {Madison}, {April} 21-23, 1958",
title = "Extremal approximations --- a summary",
volume = "no. 1",
publisher = "The University of Wisconsin Press",
address = "Madison, WI, USA",
pages = "329--340",
year = "1959",
MRclass = "65.00",
MRnumber = "101613",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
note = "Edited by R. E. Langer",
series = "Publication of the Mathematics Research Center, U.S.
Army, the University of Wisconsin",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Salzer:1959:TOI,
author = "H. E. Salzer",
title = "Tables of Osculatory Interpolation Coefficients",
volume = "56",
publisher = pub-USGPO,
address = pub-USGPO:adr,
pages = "xi + 25",
year = "1959",
MRclass = "65.00",
MRnumber = "103600",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
series = "National Bureau of Standards Applied Mathematics
Series",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Wilson:1959:SCL,
author = "L. B. Wilson",
title = "Solution of certain large sets of equations on
{Pegasus} using matrix methods",
journal = j-COMP-J,
volume = "2",
number = "3",
pages = "130--133",
month = mar,
year = "1959",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/2.3.130",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65.00",
MRnumber = "107359",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Anonymous:1960:BFP,
author = "Anonymous",
title = "{Bessel} Functions. {Part III}: {Zeros} and Associated
Values",
volume = "7",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "lx + 79",
year = "1960",
MRclass = "65.00",
MRnumber = "119441",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
note = "Prepared under the direction of the Bessel Functions
Panel of the Mathematical Tables Committee",
series = "Royal Society Mathematical Tables",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Dennis:1960:NIO,
author = "S. C. R. Dennis",
title = "The numerical integration of ordinary differential
equations possessing exponential type solutions",
journal = j-MATH-PROC-CAMB-PHILOS-SOC,
volume = "56",
number = "3",
pages = "240--246",
month = jul,
year = "1960",
CODEN = "MPCPCO",
DOI = "https://doi.org/10.1017/S0305004100034526",
ISSN = "0305-0041 (print), 1469-8064 (electronic)",
ISSN-L = "0305-0041",
MRclass = "65.00",
MRnumber = "119423",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Proceedings of the Cambridge
Philosophical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Elliott:1960:NSI,
author = "David Elliott",
title = "The numerical solution of integral equations using
{Chebyshev} polynomials",
journal = j-J-AUSTRALIAN-MATH-SOC,
volume = "1",
number = "3",
pages = "344--356",
month = aug,
year = "1960",
CODEN = "JAUMAX",
DOI = "https://doi.org/10.1017/S144678870002601X",
ISSN = "0004-9735 (print), 2059-9234 (electronic)",
ISSN-L = "0004-9735",
MRclass = "65.75",
MRnumber = "128087",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Austral. Math. Soc.",
fjournal = "Journal of the Australian Mathematical Society",
journal-URL = "https://www.cambridge.org/core/journals/journal-of-the-australian-mathematical-society",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Hammer:1960:QFI,
author = "Preston C. Hammer and Howard H. Wicke",
title = "Quadrature formulas involving derivatives of the
integrand",
journal = j-MATH-COMPUT,
volume = "14",
number = "69",
pages = "3--7",
month = jan,
year = "1960",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1960-0110191-0",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.00",
MRnumber = "110191",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
URL = "http://links.jstor.org/sici?sici=0025-5718(196001)14:69<3:QFIDOT>2.0.CO;2-O&origin=MSN",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@InCollection{Lister:1960:NSH,
author = "Mary Lister",
booktitle = "Mathematical methods for digital computers",
title = "The numerical solution of hyperbolic partial
differential equations by the method of
characteristics",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "165--179",
year = "1960",
MRclass = "68.00 (65.00)",
MRnumber = "117921",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Miller:1960:TGE,
author = "G. F. Miller",
title = "Tables of Generalized Exponential Integrals",
publisher = pub-HMSO,
address = pub-HMSO:adr,
pages = "iii + 43",
year = "1960",
MRclass = "65.05",
MRnumber = "136530",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@InCollection{Nicolovius:1960:ISB,
author = "R{\"u}diger Nicolovius",
booktitle = "Symposium on the numerical treatment of ordinary
differential equations, integral and
integro-differential equations ({Rome}, 1960)",
title = "Iterative solution of boundary value problems using
remainder terms of {Taylor} expansions",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "162--173",
year = "1960",
MRclass = "65.62",
MRnumber = "128621",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Osborne:1960:EEP,
author = "M. R. Osborne",
title = "$ h^2 $-extrapolation in eigenvalue problems",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "13",
number = "2",
pages = "156--168",
year = "1960",
CODEN = "QJMMAV",
DOI = "https://doi.org/10.1093/qjmam/13.2.156",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
MRclass = "65.00",
MRnumber = "113278",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "The Quarterly Journal of Mechanics and Applied
Mathematics",
journal-URL = "http://qjmam.oxfordjournals.org/content/by/year",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Rabinowitz:1960:AWL,
author = "Philip Rabinowitz",
title = "Abscissas and weights for {Lobatto} quadrature of high
order",
journal = j-MATH-COMPUT,
volume = "14",
number = "69",
pages = "47--52",
month = jan,
year = "1960",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1960-0110194-6",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.00",
MRnumber = "110194",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
URL = "http://links.jstor.org/sici?sici=0025-5718(196001)14:69<47:AAWFLQ>2.0.CO;2-Z&origin=MSN",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Salzer:1960:TOI,
author = "Herbert E. Salzer and Dexter C. Shoultz and Elizabeth
P. Thompson",
title = "Tables of Osculatory Integration Coefficients",
publisher = "Convair Astronautics, Division of General Dynamics
Corporation",
address = "San Diego, CA, USA",
pages = "43",
year = "1960",
MRclass = "65.05",
MRnumber = "128093",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Squire:1960:RM,
author = "William Squire",
title = "Relaxation methods",
journal = j-MATH-MAG,
volume = "33",
number = "4",
pages = "177--183",
month = mar # "\slash " # apr,
year = "1960",
CODEN = "MAMGA8",
DOI = "https://doi.org/10.2307/3029150",
ISSN = "0025-570X (print), 1930-0980 (electronic)",
ISSN-L = "0025-570X",
MRclass = "65.60",
MRnumber = "128622",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics Magazine",
journal-URL = "http://www.maa.org/pubs/mathmag.html",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Struble:1960:TUQ,
author = "George Struble",
title = "Tables for use in quadrature formulas involving
derivatives of the integrand",
journal = j-MATH-COMPUT,
volume = "14",
number = "69",
pages = "8--12",
month = jan,
year = "1960",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1960-0110192-2",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.00",
MRnumber = "110192",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
URL = "http://links.jstor.org/sici?sici=0025-5718(196001)14:69<8:TFUIQF>2.0.CO;2-T&origin=MSN",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@InCollection{Vejvoda:1960:PBV,
author = "O. Vejvoda",
booktitle = "Symposium on the numerical treatment of ordinary
differential equations, integral and
integro-differential equations ({Rome}, 1960)",
title = "Perturbed boundary-value problems and their
approximate solution",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "37--41",
year = "1960",
MRclass = "34.53",
MRnumber = "126030",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Bickley:1961:FDM,
author = "W. G. Bickley and S. Michaelson and M. R. Osborne",
title = "On finite-difference methods for the numerical
solution of boundary-value problems",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "262",
number = "1309",
pages = "219--236",
month = jul,
year = "1961",
CODEN = "PRLAAZ",
DOI = "https://doi.org/10.1098/rspa.1961.0114",
ISSN = "0962-8444 (print), 2053-9177 (electronic)",
ISSN-L = "0962-8444",
MRclass = "65.66",
MRnumber = "128624",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical, Physical and Engineering Sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Haselgrove:1961:SNL,
author = "C. B. Haselgrove",
title = "The solution of non-linear equations and of
differential equations with two-point boundary
conditions",
journal = j-COMP-J,
volume = "4",
number = "3",
pages = "255--259",
month = mar,
year = "1961",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/4.3.255",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65.50 (65.62)",
MRnumber = "130114",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Jones:1961:NSC,
author = "J. G. Jones",
title = "On the numerical solution of convolution integral
equations and systems of such equations",
journal = j-MATH-COMPUT,
volume = "15",
number = "74",
pages = "131--142",
month = apr,
year = "1961",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2004219",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.00",
MRnumber = "122001",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Ledsham:1961:NIU,
author = "F. C. Ledsham",
title = "Numerical integration using sums of exponential
functions",
journal = j-MATH-COMPUT,
volume = "15",
number = "73",
pages = "48--51",
month = jan,
year = "1961",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2003090",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.00",
MRnumber = "119421",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Reuss:1961:SRR,
author = "E. Reuss and R. Irving and C. S. Yang",
title = "Some reflections on the relaxation of biharmonic
differential equations in polar coordinates",
journal = "Periodica Polytechnica. Engineering. Periodica
Polytechnica. Maschinen- und Bauwesen",
volume = "5",
pages = "335--344",
year = "1961",
ISSN = "0031-5338",
ISSN-L = "0031-5338",
MRclass = "35.06 (65.65)",
MRnumber = "137913",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "Period. Polytech. Engrg.",
fjournal = "Periodica Polytechnica. Engineering. Periodica
Polytechnica. Maschinen- und Bauwesen",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Allen:1962:ARM,
author = "D. N. de G. Allen and B. Robins",
title = "The application of relaxation methods to satisfy
normal-gradient boundary conditions associated with
three-dimensional partial differential equations",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "15",
number = "1",
pages = "43--51",
year = "1962",
CODEN = "QJMMAV",
DOI = "https://doi.org/10.1093/qjmam/15.1.53",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
MRclass = "65.66",
MRnumber = "138202",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "The Quarterly Journal of Mechanics and Applied
Mathematics",
journal-URL = "http://qjmam.oxfordjournals.org/content/by/year",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Allen:1962:RMA,
author = "D. N. de G. Allen",
title = "Relaxation methods applied to conformal
transformations",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "15",
number = "1",
pages = "35--42 (1 insert)",
year = "1962",
CODEN = "QJMMAV",
DOI = "https://doi.org/10.1093/qjmam/15.1.53",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
MRclass = "65.66",
MRnumber = "138208",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "The Quarterly Journal of Mechanics and Applied
Mathematics",
journal-URL = "http://qjmam.oxfordjournals.org/content/by/year",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Allen:1962:SAF,
author = "D. N. de G. Allen",
title = "A suggested approach to finite-difference
representation of differential equations, with an
application to determine temperature-distributions near
a sliding contact",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "15",
number = "1",
pages = "11--33",
year = "1962",
CODEN = "QJMMAV",
DOI = "https://doi.org/10.1093/qjmam/15.1.53",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
MRclass = "65.61",
MRnumber = "138201",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "The Quarterly Journal of Mechanics and Applied
Mathematics",
journal-URL = "http://qjmam.oxfordjournals.org/content/by/year",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Treuenfels:1962:SLR,
author = "P. Treuenfels",
title = "{Schranken f{\"u}r L{\"o}sungen von Randwertaufgaben}.
({German}) [{Bounds} for solutions to boundary-value
problems]",
journal = j-NUM-MATH,
volume = "4",
number = "1",
pages = "21--23",
month = dec,
year = "1962",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01386293",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.62",
MRnumber = "136520",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
language = "German",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Griffin:1963:NSP,
author = "D. S. Griffin and R. S. Varga",
title = "Numerical Solution of Plane Elasticity Problems",
journal = j-J-SIAM,
volume = "11",
number = "4",
pages = "1046--1062",
month = dec,
year = "1963",
CODEN = "JSIMAV",
DOI = "https://doi.org/10.1137/0111077",
ISSN = "0368-4245 (print), 1095-712X (electronic)",
ISSN-L = "0368-4245",
MRclass = "65.66",
MRnumber = "160331",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib;
https://www.math.utah.edu/pub/tex/bib/siam.bib;
https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
JSTOR database",
note = "See remark \cite{Bueckner:1966:RPD}.",
URL = "http://www.math.kent.edu/~varga/pub/paper_24.pdf",
acknowledgement = ack-nhfb,
author-dates = "Richard S. Varga (8 October 1928--25 February 2022)",
fjournal = "Journal of the Society for Industrial and Applied
Mathematics",
journal-URL = "http://epubs.siam.org/loi/smjmap.1",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Dennis:1964:EEP,
author = "S. C. R. Dennis",
title = "$ h^2 $- and $ h^4 $-extrapolation in eigenvalue
problems",
journal = j-MATH-PROC-CAMB-PHILOS-SOC,
volume = "60",
number = "1",
pages = "67--74",
month = jan,
year = "1964",
CODEN = "MPCPCO",
DOI = "https://doi.org/10.1017/S0305004100037464",
ISSN = "0305-0041 (print), 1469-8064 (electronic)",
ISSN-L = "0305-0041",
MRclass = "65.62",
MRnumber = "159429",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Proceedings of the Cambridge
Philosophical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Dodes:1964:NAS,
author = "Irving Allen Dodes and Samuel L. Greitzer",
title = "Numerical Analysis. {With} scientific applications",
publisher = pub-HAYDEN-BOOK,
address = pub-HAYDEN-BOOK:adr,
pages = "ix + 390",
year = "1964",
MRclass = "65.00",
MRnumber = "175274",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Mayers:1964:DAL,
author = "D. F. Mayers",
title = "The deferred approach to the limit in ordinary
differential equations",
journal = j-COMP-J,
volume = "7",
number = "1",
pages = "54--57",
month = jan,
year = "1964",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/7.1.54",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65.60",
MRnumber = "181107",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Osborne:1964:MFD,
author = "M. R. Osborne",
title = "A method for finite-difference approximation to
ordinary differential equations",
journal = j-COMP-J,
volume = "7",
number = "1",
pages = "58--65",
month = jan,
year = "1964",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/7.1.58",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65.60",
MRnumber = "181109",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Osborne:1964:NMS,
author = "M. R. Osborne",
title = "A new method for the solution of eigenvalue problems",
journal = j-COMP-J,
volume = "7",
number = "3",
pages = "228--232",
month = mar,
year = "1964",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/7.3.228",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65.40",
MRnumber = "182142",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Singer:1964:ENA,
author = "James Singer",
title = "Elements of Numerical Analysis",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "x + 395",
year = "1964",
MRclass = "65.00",
MRnumber = "165652",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
series = "Academic Press Textbooks in Mathematics",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Conte:1965:ENA,
author = "S. D. Conte",
title = "Elementary Numerical Analysis: an Algorithmic
Approach",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "x + 278",
year = "1965",
MRclass = "65.00",
MRnumber = "202267",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Gear:1965:HMI,
author = "C. W. Gear",
title = "Hybrid methods for initial value problems in ordinary
differential equations",
journal = j-SIAM-J-NUM-ANALYSIS-B,
volume = "2",
number = "1",
pages = "69--86",
year = "1965",
DOI = "https://doi.org/10.1137/07020",
ISSN = "0887-459X (print), 2168-3581 (electronic)",
ISSN-L = "0887-459X",
MRclass = "34.04 (39.20)",
MRnumber = "179490",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Soc. Indust. Appl. Math. Ser. B Numer. Anal.",
fjournal = "Journal of the Society for Industrial and Applied
Mathematics. Series B. Numerical Analysis",
journal-URL = "http://epubs.siam.org/loi/sjnaam.1",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Goodwin:1965:NPC,
author = "E. T. Goodwin",
title = "Note on a paper by {S. C. R. Dennis}",
journal = j-MATH-PROC-CAMB-PHILOS-SOC,
volume = "61",
number = "1",
pages = "299",
month = jan,
year = "1965",
CODEN = "MPCPCO",
DOI = "https://doi.org/10.1017/s0305004100038895",
ISSN = "0305-0041 (print), 1469-8064 (electronic)",
ISSN-L = "0305-0041",
MRclass = "65.62",
MRnumber = "170478",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Proceedings of the Cambridge
Philosophical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Green:1965:SSC,
author = "D. J. Green and S. Michaelson",
title = "Series solution of certain {Sturm--Liouville}
eigenvalue problems",
journal = j-COMP-J,
volume = "7",
number = "4",
pages = "322--336",
month = jan,
year = "1965",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/7.4.322",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65.62",
MRnumber = "173361",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Pereyra:1965:CDM,
author = "Victor Pereyra",
title = "The correction difference method for non-linear
boundary value problems of class {$M$}",
journal = "Revista de la Uni{\'o}n Matem{\'a}tica Argentina",
volume = "22",
number = "4",
pages = "184--201",
year = "1965",
ISSN = "0041-6932 (print), 1669-9637 (electronic)",
ISSN-L = "0041-6932",
MRclass = "65.62",
MRnumber = "202324",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "Rev. Un. Mat. Argentina",
fjournal = "Revista de la Uni{\'o}n Matem{\'a}tica Argentina",
journal-URL = "https://inmabb.criba.edu.ar/revuma/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Clark:1966:FDR,
author = "M. M. Clark",
title = "Finite-difference representation of partial
differential equations",
journal = "Buletinul Institutului Politehnic din Ia{\c{s}}i.
Serie Nou{\u{a}}",
volume = "12/16",
pages = "31--37",
year = "1966",
ISSN = "0032-6100",
ISSN-L = "0032-6100",
MRclass = "65.65",
MRnumber = "213038",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "Bul. Inst. Politehn. Ia\c{s}i (N.S.)",
fjournal = "Buletinul Institutului Politehnic din Ia{\c{s}}i.
Serie Nou{\u{a}}",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Guderley:1966:RTP,
author = "Karl G. Guderley and Paul J. Nikolai",
title = "Reduction of two-point boundary value problems in a
vector space to inital value problems by projection",
journal = j-NUM-MATH,
volume = "8",
number = "3",
pages = "270--289",
month = may,
year = "1966",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02162563",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.62",
MRnumber = "202319",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Ilioi:1966:EER,
author = "C. Ilioi",
title = "Sur l'{\'e}valuation de l'erreur dans la
r{\'e}solution des syst{\`e}mes lin{\'e}aires",
journal = "Analele {\c{S}}tiin{\c{t}}ifice ale
Universit{\u{a}}{\c{t}}ii ``Al. I. Cuza'' din Iasi.
Sec{\c{t}}iunea I a. Matematic{\u{a}}. Serie
Nou{\u{a}}",
volume = "12",
pages = "313--320",
year = "1966",
ISSN = "0041-9109",
ISSN-L = "0041-9109",
MRclass = "65.35",
MRnumber = "223077",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "An. {\c{S}}ti. Univ. ``Al. I. Cuza'' Ia{\c{s}}i
Sec{\c{t}}. I a Mat. (N.S.)",
fjournal = "Analele {\c{S}}tiin{\c{t}}ifice ale
Universit{\u{a}}{\c{t}}ii ``Al. I. Cuza'' din Iasi.
Sec{\c{t}}iunea I a. Matematic{\u{a}}. Serie
Nou{\u{a}}",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Nickel:1967:ERP,
author = "Karl L. E. Nickel",
title = "Extension of a recent paper by {Fox}, {Henrici} and
{Moler} on eigenvalues of elliptic operators",
journal = j-SIAM-J-NUMER-ANAL,
volume = "4",
number = "4",
pages = "483--488",
month = dec,
year = "1967",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0704043",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65.66",
MRnumber = "221771",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992); Peter
Karl Henrici (13 September 1923--13 March 1987)",
}
@Article{Pereyra:1967:ACD,
author = "Victor Pereyra",
title = "Accelerating the convergence of discretization
algorithms",
journal = j-SIAM-J-NUMER-ANAL,
volume = "4",
number = "4",
pages = "508--533",
month = dec,
year = "1967",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0704046",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65.10",
MRnumber = "221726",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Andrew:1968:NRM,
author = "A. L. Andrew",
title = "A note on the {Ritz} method with an application to
overtone stellar pulsation theory",
journal = j-J-AUSTRALIAN-MATH-SOC,
volume = "8",
number = "2",
pages = "275--286",
month = may,
year = "1968",
CODEN = "JAUMAX",
DOI = "https://doi.org/10.1017/S1446788700005334",
ISSN = "0004-9735 (print), 2059-9234 (electronic)",
ISSN-L = "0004-9735",
MRclass = "65.49",
MRnumber = "234624",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Austral. Math. Soc.",
fjournal = "Journal of the Australian Mathematical Society",
journal-URL = "https://www.cambridge.org/core/journals/journal-of-the-australian-mathematical-society",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Brenner:1968:NRL,
author = "J. L. Brenner",
title = "New root-location theorems for partitioned matrices",
journal = j-SIAM-J-APPL-MATH,
volume = "16",
number = "5",
pages = "889--898",
month = sep,
year = "1968",
CODEN = "SMJMAP",
DOI = "https://doi.org/10.1137/0116072",
ISSN = "0036-1399 (print), 1095-712x (electronic)",
ISSN-L = "0036-1399",
MRclass = "65.35",
MRnumber = "239738",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Chaves:1968:NST,
author = "T. Chaves and E. L. Ortiz",
title = "On the numerical solution of two-point boundary value
problems for linear differential equations",
journal = j-Z-ANGE-MATH-MECH,
volume = "48",
number = "6",
pages = "415--418",
month = jan,
year = "1968",
CODEN = "ZAMMAX",
DOI = "https://doi.org/10.1002/zamm.19680480607",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
MRclass = "65.62",
MRnumber = "246520",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik. Ingenieurwissenschaftliche
Forschungsarbeiten",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Falkenberg:1968:MIU,
author = "J. C. Falkenberg",
title = "A method for integration of unstable systems of
ordinary differential equation subject to two-point
boundary conditions",
journal = j-BIT,
volume = "8",
number = "4",
pages = "86--103",
month = oct,
year = "1968",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/bf00144993",
ISSN = "0901-246X",
ISSN-L = "0006-3835",
MRclass = "65.62",
MRnumber = "239766",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Nordisk Tidskrift for Informationsbehandling",
journal-URL = "http://link.springer.com/journal/10543",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Iri:1968:MMD,
author = "Masao Iri",
title = "A method of multi-dimensional linear interpolation",
journal = "Information Processing in Japan",
volume = "8",
pages = "33--36",
year = "1968",
ISSN = "0537-6246",
ISSN-L = "0537-6246",
MRclass = "65.20",
MRnumber = "258239",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Inform. Process. Japan",
fjournal = "Information Processing in Japan",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Klerer:1968:ERT,
author = "Melvin Klerer and Fred Grossman",
title = "Error rates in tables of indefinite integrals",
journal = j-IND-MATH,
volume = "18",
pages = "31--62",
year = "1968",
CODEN = "IMTHAI",
ISSN = "0019-8528",
ISSN-L = "0019-8528",
MRclass = "65.05",
MRnumber = "277081",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Industrial Mathematics",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Lieberstein:1968:CNA,
author = "H. Melvin Lieberstein",
title = "A Course in Numerical Analysis",
publisher = pub-HARPER-ROW,
address = pub-HARPER-ROW:adr,
pages = "xiv + 258",
year = "1968",
MRclass = "65.00",
MRnumber = "228145",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Stenger:1968:KPE,
author = "Frank Stenger",
title = "{Kronecker} product extensions of linear operators",
journal = j-SIAM-J-NUMER-ANAL,
volume = "5",
number = "2",
pages = "422--435",
month = jun,
year = "1968",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0705033",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65.35",
MRnumber = "235711",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Yamamoto:1968:LAT,
author = "Tetsuro Yamamoto",
title = "On {Lanczos}' algorithm for tri-diagonalization",
journal = "Journal of Science of the Hiroshima University. Series
A-I. Mathematics",
volume = "32",
pages = "259--284",
year = "1968",
ISSN = "0386-3026",
ISSN-L = "0386-3026",
MRclass = "65.35",
MRnumber = "245193",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Sci. Hiroshima Univ. Ser. A-I Math.",
fjournal = "Journal of Science of the Hiroshima University. Series
A-I. Mathematics",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Rainey:1969:CST,
author = "John W. Rainey",
title = "On comparatively stable tridiagonalization methods",
journal = j-NUM-MATH,
volume = "13",
number = "4",
pages = "316--322",
month = aug,
year = "1969",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02165406",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.35",
MRnumber = "251889",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Wigley:1969:MSS,
author = "Neil M. Wigley",
title = "On a method to subtract off a singularity at a corner
for the {Dirichlet} or {Neumann} problem",
journal = j-MATH-COMPUT,
volume = "23",
number = "106",
pages = "395--401",
month = apr,
year = "1969",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2004432",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.66",
MRnumber = "245223",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Chu:1970:PPP,
author = "Shih-chi Chu",
title = "Piecewise polynomials and the partition method for
nonlinear ordinary differential equations",
journal = j-J-ENG-MATH,
volume = "4",
pages = "65--76",
year = "1970",
CODEN = "JLEMAU",
DOI = "https://doi.org/10.1007/BF01535180",
ISSN = "0022-0833 (print), 1573-2703 (electronic)",
ISSN-L = "0022-0833",
MRclass = "65.60",
MRnumber = "258286",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Engineering Mathematics",
journal-URL = "http://www.springerlink.com/content/0022-0833",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Iwata:1970:AFM,
author = "Giiti Iwata",
title = "Approximate formulas for the mean value of a function
over a tetrahedron",
journal = "Natural Science Report of the Ochanomizu University",
volume = "21",
pages = "39--47",
year = "1970",
CODEN = "NASOA5",
ISSN = "0029-8190",
ISSN-L = "0029-8190",
MRclass = "65.55",
MRnumber = "275670",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
URL = "https://teapot.lib.ocha.ac.jp/records/34934",
acknowledgement = ack-nhfb,
ajournal = "Natur. Sci. Rep. Ochanomizu Univ.",
fjournal = "Natural Science Report of the Ochanomizu University",
journal-URL = "http://www.lib.ocha.ac.jp/oab/12shizenkagaku/listOfIssue.html",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Nedyalkov:1970:ATI,
author = "I. P. Nedyalkov",
title = "An approach in the theory of incorrect problems",
journal = j-C-R-ACAD-BULGARE-SCI,
volume = "23",
pages = "5--8",
year = "1970",
CODEN = "DBANAD",
ISSN = "0366-8681",
ISSN-L = "0366-8681",
MRclass = "65.30",
MRnumber = "261772",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Doklady Bolgarsko\u{\i} Akademii Nauk. Comptes Rendus
de l'Acad{\'e}mie Bulgare des Sciences",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Romanowski:1970:IMN,
author = "M. Romanowski and L. Isaacs",
title = "Integration of modulated normal functions",
journal = "Bulletin G{\'e}od{\'e}sique (N.S.)",
number = "98",
pages = "299--308",
year = "1970",
DOI = "https://doi.org/10.1007/bf02522164",
ISSN = "0007-4632",
ISSN-L = "0007-4632",
MRclass = "65.25",
MRnumber = "275636",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "Bull. G{\'e}od{\'e}sique (N.S.)",
fjournal = "Bull. G{\'e}od{\'e}sique (N.S.)",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Takahasi:1970:EEN,
author = "Hidetosi Takahasi and Masatake Mori",
title = "Error estimation in the numerical integration of
analytic functions",
journal = "Report of the Computer Centre. University of Tokyo",
volume = "3",
pages = "41--108",
year = "1970",
CODEN = "TUCRA4",
ISSN = "0564-8742",
ISSN-L = "0564-8742",
MRclass = "65D30",
MRnumber = "295575",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "Rep. Comput. Centre Univ. Tokyo",
fjournal = "Report of the Computer Centre. University of Tokyo",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Andrew:1971:CEC,
author = "A. L. Andrew and G. C. Elton",
title = "Computation of eigenvectors corresponding to multiple
eigenvalues",
journal = j-BULL-AUSTRAL-MATH-SOC,
volume = "4",
pages = "419--422",
year = "1971",
CODEN = "ALNBAB",
DOI = "https://doi.org/10.1017/S0004972700046761",
ISSN = "0004-9727 (print), 1755-1633 (electronic)",
ISSN-L = "0004-9727",
MRclass = "65.40",
MRnumber = "281332",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the Australian Mathematical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BAZ",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Dekker:1971:ASA,
author = "T. J. Dekker and J. F. Traub",
title = "An analysis of the shifted {$ L R $} algorithm",
journal = j-NUM-MATH,
volume = "17",
number = "3",
pages = "179--188",
month = jun,
year = "1971",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01436374",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F15",
MRnumber = "297117",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Grad:1971:MB,
author = "J. Grad",
title = "Matrix balancing",
journal = j-COMP-J,
volume = "14",
number = "3",
pages = "280--284",
month = mar,
year = "1971",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/14.3.280",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65F15",
MRnumber = "398082",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Keeping:1971:CAT,
author = "A. J. Keeping",
title = "On certain almost-triangular band matrices",
journal = j-SIAM-J-NUMER-ANAL,
volume = "8",
number = "2",
pages = "288--303",
month = jun,
year = "1971",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0708030",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F15",
MRnumber = "292289",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Lado:1971:NFT,
author = "F. Lado",
title = "Numerical {Fourier} transforms in one, two, and three
dimensions for liquid state calculations",
journal = j-J-COMPUT-PHYS,
volume = "8",
pages = "417--433",
year = "1971",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(71)90021-0",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
MRclass = "65D30",
MRnumber = "298886",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Stewart:1971:HRW,
author = "N. F. Stewart",
title = "A heuristic to reduce the wrapping effect in the
numerical solution of $ x^\prime = f(t, x) $",
journal = j-BIT,
volume = "11",
number = "3",
pages = "328--337",
month = sep,
year = "1971",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/bf01931814",
ISSN = "0901-246X",
ISSN-L = "0006-3835",
MRclass = "65L05",
MRnumber = "292334",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Nordisk Tidskrift for Informationsbehandling",
journal-URL = "http://link.springer.com/journal/10543",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Young:1971:ISL,
author = "David M. Young",
title = "Iterative Solution of Large Linear Systems",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xxiv + 570",
year = "1971",
ISBN = "0-12-773050-8",
ISBN-13 = "978-0-12-773050-9",
LCCN = "QA195 .Y681 1971",
MRclass = "65F10",
MRnumber = "46 4698 (305568)",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
series = "Computer Science and Applied Mathematics, Editor:
Werner Rheinboldt",
acknowledgement = ack-nhfb,
author-dates = "David M. Young, Jr. (October 20, 1923--December 21,
2008)",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
tableofcontents = "Preface / xiii \\
Acknowledgments / xvii \\
Notation / xix \\
List of Fundamental Matrix Properties / xxi \\
List of Iterative Methods / xxiii \\
Introduction / 1 \\
The Model Problem / 2 \\
Supplementary Discussion / 6 \\
Exercises / 6 \\
Matrix Preliminaries / 7 \\
Review of Matrix Theory / 7 \\
Hermitian Matrices and Positive Definite Matrices / 18
\\
Vector Norms and Matrix Norms / 25 \\
Convergence of Sequences of Vectors and Matrices / 34
\\
Irreducibility and Weak Diagonal Dominance / 36 \\
Property $A$ / 41 \\
L-Matrices and Related Matrices / 42 \\
Illustrations / 48 \\
Supplementary Discussion / 53 \\
Exercises / 55 \\
Linear Stationary Iterative Methods / 63 \\
Introduction / 63 \\
Consistency, Reciprocal Consistency, and Complete
Consistency / 65 \\
Basic Linear Stationary Iterative Methods / 70 \\
Generation of Completely Consistent Methods / 75 \\
General Convergence Theorems / 77 \\
Alternative Convergence Conditions / 80 \\
Rates of Convergence / 84 \\
The Jordan Condition Number of a $2 \times 2$ Matrix /
89 \\
Supplementary Discussion / 94 \\
Exercises / 95 \\
Convergence of the Basic Iterative Methods / 106 \\
General Convergence Theorems / 106 \\
Irreducible Matrices with Weak Diagonal Dominance / 107
\\
Positive Definite Matrices / 108 \\
The SOR Method with Varying Relaxation Factors / 118
\\
L-Matrices and Related Matrices / 120 \\
Rates of Convergence of the J and GS Methods for the
Model Problem / 127 \\
Supplementary Discussion / 132 \\
Exercises / 133 \\
Eigenvalues of the SOR Method for Consistently Ordered
Matrices / 140 \\
Introduction / 140 \\
Block Tri-Diagonal Matrices / 141 \\
Consistently Ordered Matrices and Ordering Vectors /
144 \\
Property $A$ / 148 \\
Nonmigratory Permutations / 153 \\
Consistently Ordered Matrices Arising from Difference
Equations / 157 \\
A Computer Program for Testing for Property $A$ and
Consistent Ordering / 159 \\
Other Developments of the SOR Theory / 162 \\
Supplementary Discussion / 163 \\
Exercises / 163 \\
Determination of the Optimum Relaxation Factor / 169
\\
Virtual Spectral Radius / 170 \\
Analysis of the Case Where All Eigenvalues of B Are
Real / 171 \\
Rates of Convergence: Comparison with the Gauss--Seidel
Method / 188 \\
Analysis of the Case Where Some Eigenvalues of B Are
Complex / 191 \\
Practical Determination of $\omega_b$: General
Considerations / 200 \\
Iterative Methods of Choosing $\omega_b$ / 209 \\
An Upper Bound for $\mu$ / 211 \\
A Priori Determination of $\mu$: Exact Methods / 216
\\
A Priori Determination of $\mu$: Approximate Values /
222 \\
Numerical Results / 224 \\
Supplementary Discussion / 227 \\
Exercises / 228 \\
Norms of the SOR Method / 233 \\
The Jordan Canonical Form of ${\cal L}_\omega$ / 234
\\
Basic Eigenvalue Relation / 239 \\
Determination of $||{\cal L}_\omega||_{D^{1/2}}$ / 245
\\
Determination of $||{\cal L}^m_{\omega_b}||_{D^{1/2}}$
/ 248 \\
Determination of $||{\cal L}_\omega||_{A^{1/2}}$ / 255
\\
Determination of $||{\cal L}^m_{\omega_b}||_{A^{1/2}}$
/ 258 \\
Comparison of $||{\cal L}^m_{\omega_b}||_{D^{1/2}}$ and
$||{\cal L}^m_{\omega_b}||_{A^{1/2}}$ / 264 \\
Supplementary Discussion / 265 \\
Exercises / 266 \\
The Modified SOR Method: Fixed Parameters / 271 \\
Introduction / 271 \\
Eigenvalues of ${\cal L}_{\omega, \omega'}$ / 273 \\
Convergence and Spectral Radius / 277 \\
Determination of $||{\cal L}_{\omega,
\omega'}_{D^{1/2}}||$ / 283 \\
Determination of $||{\cal L}_{\omega,
\omega'}_{A^{1/2}}||$ / 288 \\
Supplementary Discussion / 291 \\
Exercises / 291 \\
Nonstationary Linear Iterative Methods / 295 \\
Consistency, Convergence, and Rates of Convergence /
295 \\
Periodic Nonstationary Methods / 300 \\
Chebyshev Polynomials / 301 \\
Supplementary Discussion / 304 \\
Exercises / 304 \\
The Modified SOR Method: Variable Parameters / 306 \\
Convergence of the MSOR Method / 307 \\
Optimum Choice of Relaxation Factors / 307 \\
Alternative Optimum Parameter Sets / 311 \\
Norms of the MSOR Method: Sheldon's Method / 315 \\
The Modified Sheldon Method / 319 \\
Cyclic Chebyshev Semi-Iterative Method / 321 \\
Comparison of Norms / 327 \\
Supplementary Discussion / 340 \\
Exercises / 341 \\
Semi-Iterative Methods / 344 \\
General Considerations / 345 \\
The Case Where G Has Real Eigenvalues / 347 \\
J, JOR, and RF Semi-Iterative Methods / 355 \\
Richardson's Method / 361 \\
Cyclic Chebyshev Semi-Iterative Method / 365 \\
GS Semi-Iterative Methods / 367 \\
SOR Semi-Iterative Methods / 374 \\
MSOR Semi-Iterative Methods / 376 \\
Comparison of Norms / 383 \\
Supplementary Discussion / 385 \\
Exercises / 386 \\
Extensions of the SOR Theory: Stieltjes Matrices / 391
\\
The Need for Some Restrictions on A / 391 \\
Stieltjes Matrices / 395 \\
Supplementary Discussion / 401 \\
Exercises / 401 \\
Generalized Consistently Ordered Matrices / 404 \\
Introduction / 404 \\
${\rm CO}(q, r)$-Matrices, Property $A_{q,r}$, and
Ordering Vectors / 405 \\
Determination of the Optimum Relaxation Factor / 413
\\
Generalized Consistently Ordered Matrices / 418 \\
Relation between ${\rm GCO}(q, r)$-Matrices and ${\rm
CO}(q, r)$-Matrices / 419 \\
Computational Procedures: Canonical Forms / 422 \\
Relation to Other Work / 428 \\
Supplementary Discussion / 429 \\
Exercises / 430 \\
Group Iterative Methods / 434 \\
Construction of Group Iterative Methods / 435 \\
Solution of a Linear System with a Tri-Diagonal Matrix
/ 441 \\
Convergence Analysis / 445 \\
Applications / 452 \\
Comparison of Point and Group Iterative Methods / 454
\\
Supplementary Discussion / 456 \\
Exercises / 457 \\
Symmetric SOR Method and Related Methods / 461 \\
Introduction / 461 \\
Convergence Analysis / 463 \\
Choice of Relaxation Factor / 464 \\
SSOR Semi-Iterative Methods: The Discrete Dirichlet
Problem / 471 \\
Group SSOR Methods / 474 \\
Unsymmetric SOR Method / 476 \\
Symmetric and Unsymmetric MSOR Methods / 478 \\
Supplementary Discussion / 480 \\
Exercises / 481 \\
Second-Degree Methods / 486 \\
Supplementary Discussion / 493 \\
Exercises / 493 \\
Alternating Direction Implicit Methods / 495 \\
Introduction: The Peaceman--Rachford Method / 495 \\
The Stationary Case: Consistency and Convergence / 498
\\
The Stationary Case: Choice of Parameters / 503 \\
The Commutative Case / 514 \\
Optimum Parameters / 518 \\
Good Parameters / 525 \\
The Helmholtz Equation in a Rectangle / 531 \\
Monotonicity / 534 \\
Necessary and Sufficient Conditions for the Commutative
Case / 535 \\
The Noncommutative Case / 545 \\
Supplementary Discussion / 547 \\
Exercises / 548 \\
Selection of Iterative Method / 553 \\
Bibliography / 556 \\
Index / 565",
}
@Article{Boland:1972:NSF,
author = "W. Robert Boland",
title = "The numerical solution of {Fredholm} integral
equations using product type quadrature formulas",
journal = j-BIT,
volume = "12",
number = "1",
pages = "5--16",
month = mar,
year = "1972",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/bf01932669",
ISSN = "0901-246X",
ISSN-L = "0006-3835",
MRclass = "65R05",
MRnumber = "312758",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Nordisk Tidskrift for Informationsbehandling",
journal-URL = "http://link.springer.com/journal/10543",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Goldfarb:1972:MMI,
author = "D. Goldfarb",
title = "Modification methods for inverting matrices and
solving systems of linear algebraic equations",
journal = j-MATH-COMPUT,
volume = "26",
number = "120",
pages = "829--852",
month = oct,
year = "1972",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2005866",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F10 (65F30)",
MRnumber = "317527",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Kuki:1972:AAC,
author = "Hirondo Kuki",
title = "{ACM Algorithm 421}: Complex Gamma Function with Error
Control [{S14}]",
journal = j-CACM,
volume = "15",
number = "4",
pages = "271--272",
month = apr,
year = "1972",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/361284.361296",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65D20",
MRnumber = "47 1249",
MRreviewer = "L. Fox",
bibdate = "Mon Jan 22 06:56:30 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Kuki72a;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran1.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4130 (Interpolation and function approximation);
C7310 (Mathematics computing)",
corpsource = "Univ. Chicago, IL, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "algorithm; complex; complex gamma function; complex
loggamma; error control; FORTRAN; function; function
approximation; loggamma function; programme;
subroutines",
oldlabel = "Kuki72a",
remark = "Fullerton: 100-line FORTRAN routine with double
complex accuracy to $ 10^{-14} $.",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kuki72a",
}
@Article{Kuki:1972:CGF,
author = "Hirondo Kuki",
title = "Complex Gamma Function with Error Control [{S14}]",
journal = j-CACM,
volume = "15",
number = "4",
pages = "262--267",
month = apr,
year = "1972",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/361284.361296",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65D20",
MRnumber = "47 1249 (312693)",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Kuki72a;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran1.bib",
acknowledgement = ack-nhfb,
citedby = "Fullerton:1980:BEM",
classcodes = "C4130 (Interpolation and function approximation);
C7310 (Mathematics computing)",
corpsource = "Univ. Chicago, IL, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "algorithm; complex; complex gamma function; complex
loggamma; error control; FORTRAN; function; function
approximation; loggamma function; programme;
subroutines",
oldlabel = "Kuki72a",
remark = "Fullerton: Description of a FORTRAN routine with some
math details.",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kuki72a",
}
@Article{Pelios:1972:MEC,
author = "A. Pelios and R. W. Klopfenstein",
title = "Minimal error constant numerical differentiation
({N.D}.) formulas",
journal = j-MATH-COMPUT,
volume = "26",
number = "118",
pages = "467--475",
month = apr,
year = "1972",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2005173",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D25",
MRnumber = "307441",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Steinberg:1972:NSV,
author = "J. Steinberg",
title = "Numerical solution of {Volterra} integral equation",
journal = j-NUM-MATH,
volume = "19",
number = "3",
pages = "212--217",
month = jun,
year = "1972",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01404691",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65R05",
MRnumber = "305637",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Usmani:1972:MSM,
author = "Riaz A. Usmani",
title = "A multi-step method for the numerical integration of
ordinary differential equations",
journal = j-Z-ANGE-MATH-PHYS,
volume = "23",
number = "3",
pages = "465--483",
month = may,
year = "1972",
CODEN = "ZAMPDB",
DOI = "https://doi.org/10.1007/BF01595484",
ISSN = "0044-2275 (print), 1420-9039 (electronic)",
ISSN-L = "0044-2275",
MRclass = "65L05",
MRnumber = "312736",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Zeitschrift f{\"u}r Angewandte Mathematik und Physik.
ZAMP. Journal of Applied Mathematics and Physics.
Journal de Math{\'e}matiques et de Physique
Appliqu{\'e}es",
journal-URL = "http://link.springer.com/journal/33",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@InCollection{Anderssen:1973:CND,
author = "R. S. Anderssen",
booktitle = "Error, approximation, and accuracy ({Proc}. {Sem}.,
{Austral}. {Nat}. {Univ}., {Canberra}, 1972)",
title = "Computing with noisy data with an application to
{Abel}'s equation",
publisher = "University of Queensland Press",
address = "St. Lucia, Brisbane, QLD, Australia",
pages = "61--80",
year = "1973",
MRclass = "65D99",
MRnumber = "428690",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@InCollection{Broyden:1973:QNM,
author = "C. G. Broyden",
booktitle = "Numerical solution of systems of nonlinear algebraic
equations ({NSF-CBMS Regional Conf., Univ. Pittsburgh,
Pittsburgh, Pa., 1972})",
title = "Quasi-{Newton}, or modification methods",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "241--280",
year = "1973",
MRclass = "65H10",
MRnumber = "408233",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{DellaTorre:1973:CPS,
author = "E. {Della Torre} and W. Kinsner",
title = "Convergence properties of the successive extrapolated
relaxation ({S.E.R.}) method",
journal = j-J-INST-MATH-APPL,
volume = "12",
number = "3",
pages = "175--185",
month = oct,
year = "1973",
CODEN = "JMTAA8",
DOI = "https://doi.org/10.1093/imamat/12.2.175",
ISSN = "0020-2932",
ISSN-L = "0020-2932",
MRclass = "65F10",
MRnumber = "50 #15304 (362866)",
MRreviewer = "L. Fox",
bibdate = "Sat Apr 6 16:27:10 2002",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/jinstmathappl.bib",
ZMnumber = "0266.65006",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Institute of Mathematics and its
Applications",
journal-URL = "http://imamat.oxfordjournals.org/content/by/year",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Fazekas:1973:MAT,
author = "F. Fazekas",
title = "Matrix algorithms for tasks connected with symmetrical
matrices",
journal = j-Z-ANGE-MATH-MECH,
volume = "53",
number = "12",
pages = "T186--T188",
month = jan,
year = "1973",
CODEN = "ZAMMAX",
DOI = "https://doi.org/10.1002/zamm.19730531296",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
MRclass = "65F05",
MRnumber = "353642",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik. Ingenieurwissenschaftliche
Forschungsarbeiten",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Hwang:1973:RRS,
author = "W. G. Hwang and John Todd",
title = "A recurrence relation for the square root",
journal = j-J-APPROX-THEORY,
volume = "9",
number = "4",
pages = "299--306",
month = dec,
year = "1973",
CODEN = "JAXTAZ",
DOI = "https://doi.org/10.1016/0021-9045(73)90075-0",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
MRclass = "65H05",
MRnumber = "373270",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0271.65032",
acknowledgement = ack-nhfb,
author-dates = "John Todd (16 May 1911--21 June 2007)",
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
received = "19 April 1971",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
ZBmath = "3426800",
}
@Article{Kulikov:1973:EEA,
author = "{\`E}. L. Kulikov",
title = "Estimating errors in the approximate solution of
boundary value problems in electrodynamics by the
variational method",
journal = "Radio Engineering and Electronic Physics. A
translation of Radiotekhnika i {\`E}lektronika, a
U.S.S.R. Academy of Sciences Publication",
volume = "18",
pages = "926--929",
year = "1973",
ISSN = "0033-7889",
ISSN-L = "0033-7889",
MRclass = "65N15",
MRnumber = "418478",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "Radio Engrg. Electron. Phys.",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Scraton:1973:PAS,
author = "R. E. Scraton",
title = "Polynomial approximations to the solution of the heat
equation",
journal = j-MATH-PROC-CAMB-PHILOS-SOC,
volume = "73",
number = "1",
pages = "157--165",
month = jan,
year = "1973",
CODEN = "MPCPCO",
DOI = "https://doi.org/10.1017/s0305004100047563",
ISSN = "0305-0041 (print), 1469-8064 (electronic)",
ISSN-L = "0305-0041",
MRclass = "65P05 (35K05)",
MRnumber = "312755",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Proceedings of the Cambridge
Philosophical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Shimizu:1973:NID,
author = "Tatsujiro Shimizu",
title = "Numerical integration of differential equations on $ 0
\leq x < \infty $",
journal = "TRU Mathematics",
volume = "9",
pages = "63--67",
year = "1973",
ISSN = "0496-6597",
ISSN-L = "0496-6597",
MRclass = "65L05",
MRnumber = "349022",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "TRU Math.",
fjournal = "TRU Mathematics",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Chang:1974:FQF,
author = "Gau Zu Chang",
title = "On the {Filon} quadrature and {Fast Fourier Transform
(FFT)} algorithm",
journal = "Bulletin of the Institute of Mathematics. Academia
Sinica",
volume = "2",
number = "1",
pages = "21--27",
year = "1974",
ISSN = "0304-9825 (print), 2304-7917 (electronic)",
ISSN-L = "0304-9825",
MRclass = "65D30",
MRnumber = "348978",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "Bull. Inst. Math. Acad. Sinica",
fjournal = "Bulletin of the Institute of Mathematics. Academia
Sinica",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{deHoog:1974:IRK,
author = "F. de Hoog and R. Weiss",
title = "Implicit {Runge--Kutta} methods for second kind
{Volterra} integral equations",
journal = j-NUM-MATH,
volume = "23",
number = "3",
pages = "199--213",
month = jun,
year = "1974",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01400303",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65R05",
MRnumber = "373349",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Gyr:1974:EPM,
author = "Marcel Gyr",
title = "Eigenvalues of partitioned matrices ``generated'' by a
matrix with known eigenvalues",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "AC-19",
pages = "88--89",
year = "1974",
CODEN = "IETAA9",
DOI = "https://doi.org/10.1109/tac.1974.1100460",
ISSN = "0018-9286 (print), 1558-2523 (electronic)",
ISSN-L = "0018-9286",
MRclass = "65F15",
MRnumber = "362869",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Institute of Electrical and Electronics Engineers.
Transactions on Automatic Control",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Hitotumatu:1974:NMC,
author = "Sin Hitotumatu",
title = "A new method for the computation of square root,
exponential and logarithmic functions through
hyperbolic {CORDIC}",
journal = "Revue d'Analyse Num{\'e}rique et de la Th{\'e}orie de
l'Approximation",
volume = "3",
number = "2",
pages = "173--180",
year = "1974",
ISSN = "1010-3376 (print), 2457-8118 (electronic)",
ISSN-L = "1010-3376",
MRclass = "65D20",
MRnumber = "381249",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "https://ictp.acad.ro/jnaat/journal/article/view/1974-vol3-no2-art7",
acknowledgement = ack-nhfb,
ajournal = "Rev. Anal. Num{\'e}r. Th{\'e}orie Approximation",
fjournal = "Revue d'Analyse Num{\'e}rique et de la Th{\'e}orie de
l'Approximation",
journal-URL = "https://ictp.acad.ro/jnaat/journal",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Holnapy:1974:NAD,
author = "D. Holnapy",
title = "Numerical algorithm to determine the difference
operators of boundary-value problems",
journal = "Acta Tech. Acad. Sci. Hungar.",
volume = "76",
pages = "413--423",
year = "1974",
ISSN = "0001-7035",
ISSN-L = "0001-7035",
MRclass = "65N05",
MRnumber = "353683",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Acta Technica Academiae Scientiarum Hungaricae",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Orlov:1974:FTN,
author = "K. Orlov",
title = "Forming of the table of numerical values of the
polynomial by two operations for each new value",
journal = "Mathematica Balkanica",
volume = "4",
pages = "473--476",
year = "1974",
ISSN = "0350-2007",
ISSN-L = "0350-2007",
MRclass = "65D20",
MRnumber = "373232",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "Math. Balkanica",
fjournal = "Mathematica Balkanica",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Orlov:1974:NKN,
author = "K. Orlov",
title = "A new kind of numerical tables of functions made by
mathematical spectra",
journal = "Mat. Vesnik",
volume = "11/26",
pages = "191--201",
year = "1974",
ISSN = "0025-5165 (print), 2406-0682 (electronic)",
ISSN-L = "0025-5165",
MRclass = "65D20",
MRnumber = "359274",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
URL = "https://gdz.sub.uni-goettingen.de/id/PPN311571026_0026",
acknowledgement = ack-nhfb,
fjournal = "Matemati\v{c}ki Vesnik",
journal-URL = "http://www.vesnik.math.rs/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@InCollection{Ortiz:1974:CPL,
author = "Eduardo L. Ortiz",
booktitle = "Studies in numerical analysis (papers in honour of
{Cornelius} {Lanczos} on the occasion of his 80th
birthday)",
title = "Canonical polynomials in the {Lanczos} tau method",
publisher = "Royal Irish Academy",
address = "Dublin, Ireland",
pages = "73--93",
year = "1974",
MRclass = "65L99 (65D20)",
MRnumber = "474847",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Pace:1974:EALa,
author = "I. S. Pace and S. Barnett",
title = "Efficient algorithms for linear system calculations.
{I}. {Smith} form and common divisor of polynomial
matrices",
journal = j-INT-J-SYST-SCI,
volume = "5",
pages = "403--411",
month = may,
year = "1974",
CODEN = "IJSYA9",
DOI = "https://doi.org/10.1080/00207727408920109",
ISSN = "0020-7721 (print), 1464-5319 (electronic)",
ISSN-L = "0020-7721",
MRclass = "65F35",
MRnumber = "362877",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Systems Science. Principles
and Applications of Systems and Integration",
journal-URL = "http://www.tandfonline.com/loi/tsys20",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Pace:1974:EALb,
author = "I. S. Pace and S. Barnett",
title = "Efficient algorithms for linear system calculations.
{II}. {Minimal} realization",
journal = j-INT-J-SYST-SCI,
volume = "5",
number = "5",
pages = "413--424",
month = may,
year = "1974",
CODEN = "IJSYA9",
DOI = "https://doi.org/10.1080/00207727408920110",
ISSN = "0020-7721 (print), 1464-5319 (electronic)",
ISSN-L = "0020-7721",
MRclass = "65F35",
MRnumber = "362878",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Systems Science. Principles
and Applications of Systems and Integration",
journal-URL = "http://www.tandfonline.com/loi/tsys20",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Bose:1975:NNT,
author = "N. K. Bose",
title = "Non-negativity test of multidimensional {Hermitian}
matrices",
journal = j-J-FRANKLIN-INST,
volume = "299",
number = "6",
pages = "453--456",
month = jun,
year = "1975",
CODEN = "JFINAB",
DOI = "https://doi.org/10.1016/0016-0032(75)90007-1",
ISSN = "0016-0032 (print), 1879-2693 (electronic)",
ISSN-L = "0016-0032",
MRclass = "65F30",
MRnumber = "373260",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Franklin Institute",
journal-URL = "http://www.sciencedirect.com/science/journal/00160032",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Gautschi:1975:OCV,
author = "Walter Gautschi",
title = "Optimally Conditioned {Vandermonde} Matrices",
journal = j-NUM-MATH,
volume = "24",
number = "1",
pages = "1--12",
month = feb,
year = "1975",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01437212",
ISSN = "0029-599x (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F35",
MRnumber = "426401",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
classification = "B0260 (Optimisation techniques); B0290H (Linear
algebra); C1180 (Optimisation techniques); C4140
(Linear algebra)",
corpsource = "Purdue Univ., W. Lafayette, IN, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "condition number; matrix algebra; minimisation;
minimize; nonlinear constraints; nonlinear minimax
problem; nonlinear programming; optimally conditioned
Vandermonde matrices; symmetric point configurations",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
treatment = "T Theoretical or Mathematical",
}
@Article{Hegedus:1975:LEI,
author = "Cs. J. Heged{\H{u}}s",
title = "{Laurent} expansion of an inverse of a function
matrix",
journal = j-PERIOD-MATH-HUNGAR,
volume = "6",
number = "1",
pages = "75--86",
month = mar,
year = "1975",
CODEN = "PMHGAW",
DOI = "https://doi.org/10.1007/BF02018398",
ISSN = "0031-5303 (print), 1588-2829 (electronic)",
ISSN-L = "0031-5303",
MRclass = "65F30",
MRnumber = "373261",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Periodica Mathematica Hungarica. Journal of the
J{\'a}nos Bolyai Mathematical Society",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Todd:1975:LC,
author = "John Todd",
title = "The Lemniscate Constants",
journal = j-CACM,
volume = "18",
number = "1",
pages = "14--19",
month = jan,
year = "1975",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/360569.360580",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "33E05 65D20",
MRnumber = "51 11935 (375745)",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "Compendex database;
http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#Todd75;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib",
note = "Collection of articles honoring {Alston S.
Householder}. See corrigendum \cite{Todd:1975:CLC}.
Reprinted in \cite{Todd:2000:LC}.",
ZMnumber = "0298.33001",
abstract = "The lemniscate constants, and indeed some of the
methods used for actually computing them, have played
an enormous part in the development of mathematics. An
account is given here of some of the methods used ---
most of the derivations can be made by elementary
methods. This material can be used for teaching
purposes, and there is much relevant and interesting
historical material. The acceleration methods developed
for the purpose of evaluating these constants are
useful in other problems.",
acknowledgement = ack-nhfb,
author-dates = "John Todd (16 May 1911--21 June 2007)",
classcodes = "B0290D (Functional analysis); B0290Z (Other numerical
methods); C4120 (Functional analysis); C4190 (Other
numerical methods)",
classification = "921",
corpsource = "California Inst. of Technol., Pasadena, CA, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "acceleration; acceleration methods; elliptic
functions; Euler transformation; function evaluation;
lemniscate; lemniscate constants; mathematical
techniques; mathematics; transforms",
oldlabel = "Todd75",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
treatment = "B Bibliography; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Todd75",
ZBmath = "3467558",
}
@Article{Tsao:1975:IRT,
author = "Nai-Kuan Tsao",
title = "On iterative refinement of triangular linear algebraic
systems",
journal = j-J-FRANKLIN-INST,
volume = "299",
number = "6",
pages = "409--416",
month = jun,
year = "1975",
CODEN = "JFINAB",
DOI = "https://doi.org/10.1016/0016-0032(75)90003-4",
ISSN = "0016-0032 (print), 1879-2693 (electronic)",
ISSN-L = "0016-0032",
MRclass = "65F10",
MRnumber = "373249",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Franklin Institute",
journal-URL = "http://www.sciencedirect.com/science/journal/00160032",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Beauwens:1976:ECP,
author = "Robert Beauwens and Lena Quenon",
title = "Existence criteria for partial matrix factorizations
in iterative methods",
journal = j-SIAM-J-NUMER-ANAL,
volume = "13",
number = "4",
pages = "615--643",
month = sep,
year = "1976",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0713052",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F10",
MRnumber = "433837",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Chaudhry:1976:NMI,
author = "Muhammad Anwar Chaudhry",
title = "Numerical methods for integro-difference equations",
journal = j-MEM-FAC-SCI-KYUSHU-UNIV-A,
volume = "30",
number = "1",
pages = "15--23",
year = "1976",
CODEN = "MFKAAF",
DOI = "https://doi.org/10.2206/kyushumfs.30.15",
ISSN = "0373-6385 (print), 1883-2172 (electronic)",
ISSN-L = "0373-6385",
MRclass = "65R05",
MRnumber = "413563",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Memoirs of the Faculty of Science. Kyushu University.
Series A. Mathematics",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Jeltsch:1976:NSM,
author = "Rolf Jeltsch",
title = "Note on {$A$}-stability of multistep multiderivative
methods",
journal = j-BIT,
volume = "16",
number = "1",
pages = "74--78",
month = mar,
year = "1976",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/bf01940779",
ISSN = "0901-246X",
ISSN-L = "0006-3835",
MRclass = "65L05",
MRnumber = "411173",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Nordisk Tidskrift for Informationsbehandling",
journal-URL = "http://link.springer.com/journal/10543",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@InCollection{Kennebrock:1976:DSN,
author = "W. Kennebrock",
booktitle = "Methoden und {Verfahren} der mathematischen {Physik},
{Band} 16",
title = "A difference scheme for the numerical solution of the
{Boltzmann}-equation",
publisher = pub-BIBLIO-INST,
address = pub-BIBLIO-INST:adr,
pages = "91--103",
year = "1976",
MRclass = "82.65 (65R05)",
MRnumber = "413960",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Kurtz:1976:SFO,
author = "Lawrence A. Kurtz and David G. Weinman and Alan K.
Cline",
title = "The solution of a fourth-order partial differential
equation using the method of lines",
journal = j-APPL-ANAL,
volume = "5",
number = "3",
pages = "201--206",
month = jan,
year = "1976",
CODEN = "APANCC",
DOI = "https://doi.org/10.1080/00036817608839122",
ISSN = "0003-6811",
ISSN-L = "0003-6811",
MRclass = "65N35",
MRnumber = "408274",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Applicable Analysis. An International Journal",
journal-URL = "https://www.tandfonline.com/loi/gapa20",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Lemeire:1976:EMO,
author = "Frans Lemeire",
title = "Equilibration of matrices to optimize backward
numerical stability",
journal = j-BIT,
volume = "16",
number = "2",
pages = "143--145",
month = jun,
year = "1976",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/bf01931366",
ISSN = "0901-246X",
ISSN-L = "0006-3835",
MRclass = "65F35",
MRnumber = "426402",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Nordisk Tidskrift for Informationsbehandling",
journal-URL = "http://link.springer.com/journal/10543",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Nakashima:1976:NMN,
author = "Katsuya Nakashima and Katsushi Ohmori and Kunio
Tsuruta",
title = "The {Newton} method for nonlinear {Volterra}
integro-differential equations",
journal = "Bulletin of Science and Engineering Research
Laboratory. Waseda University",
number = "73",
pages = "54--63",
year = "1976",
ISSN = "0372-7181",
ISSN-L = "0372-7181",
MRclass = "65R05",
MRnumber = "426470",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "Bull. Sci. Engrg. Res. Lab. Waseda Univ.",
fjournal = "Bulletin of Science and Engineering Research
Laboratory. Waseda University",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@InCollection{Bremi:1977:CAN,
author = "P. Bremi",
booktitle = "Numerical analysis ({Proc}. {Colloq}., {Lausanne},
1976)",
title = "Combination of analytical and numerical calculation
methods",
volume = "37",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "195--208",
year = "1977",
ISBN = "3-7643-0939-3",
ISBN-13 = "978-3-7643-0939-8",
MRclass = "65C99",
MRnumber = "468101",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
series = "Internat. Ser. Numer. Math.",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Hsiao:1977:GMC,
author = "George C. Hsiao and Wolfgang Wendland",
title = "On {Galerkin}'s method for a class of integral
equations of the first kind",
journal = j-APPL-ANAL,
volume = "6",
number = "2",
pages = "155--157",
month = jan,
year = "1977",
CODEN = "APANCC",
DOI = "https://doi.org/10.1080/00036817708839150",
ISSN = "0003-6811",
ISSN-L = "0003-6811",
MRclass = "65R05",
MRnumber = "443384",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Applicable Analysis. An International Journal",
journal-URL = "https://www.tandfonline.com/loi/gapa20",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Kundu:1977:AIN,
author = "M. C. Kundu",
title = "Approximate integration near a simple pole using
{Chebyshev} points of the second kind",
journal = "Bulletin Math{\'e}matique de la Soci{\'e}t{\'e} des
Sciences Math{\'e}matiques de la R{\'e}publique
Socialiste de Roumaine. Nouvelle S{\'e}rie",
volume = "21(69)",
number = "3--4",
pages = "323--330",
year = "1977",
ISSN = "0007-4691",
ISSN-L = "0007-4691",
MRclass = "65D30",
MRnumber = "474711",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
URL = "https://www.jstor.org/stable/43759449",
acknowledgement = ack-nhfb,
ajournal = "Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.)",
fjournal = "Bulletin Math{\'e}matique de la Soci{\'e}t{\'e} des
Sciences Math{\'e}matiques de la R{\'e}publique
Socialiste de Roumaine. Nouvelle S{\'e}rie",
journal-URL = "https://www.jstor.org/journal/bullmathsociscie",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Morris:1977:CPN,
author = "A. G. Morris and T. S. Horner",
title = "{Chebyshev} polynomials in the numerical solution of
differential equations",
journal = j-MATH-COMPUT,
volume = "31",
number = "140",
pages = "881--891",
month = oct,
year = "1977",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2006119",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65L10",
MRnumber = "443359",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Olaofe:1977:TMS,
author = "G. Oluremi Olaofe",
title = "On the {Tchebyschev} method of solution of ordinary
differential equations",
journal = j-J-MATH-ANAL-APPL,
volume = "60",
number = "1",
pages = "1--7",
month = aug,
year = "1977",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/0022-247X(77)90043-9",
ISSN = "0022-247x (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "65L05",
MRnumber = "443354",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Rheinboldt:1977:EMP,
author = "W. C. Rheinboldt and C. K. Mesztenyi and J. M.
Fitzgerald",
title = "On the evaluation of multivariate polynomials and
their derivatives",
journal = j-BIT,
volume = "17",
number = "4",
pages = "437--457",
month = dec,
year = "1977",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/bf01933453",
ISSN = "0901-246X",
ISSN-L = "0006-3835",
MRclass = "65D15 (68A20)",
MRnumber = "461848",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Nordisk Tidskrift for Informationsbehandling",
journal-URL = "http://link.springer.com/journal/10543",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Alt:1978:SOS,
author = "Ren{\'e} Alt",
title = "{$A$}-stable one-step methods with step-size control
for stiff systems of ordinary differential equations",
journal = j-J-COMPUT-APPL-MATH,
volume = "4",
number = "1",
pages = "29--35",
year = "1978",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0771-050X(78)90016-5",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65L05",
MRnumber = "474825",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Fairweather:1978:NEI,
author = "Graeme Fairweather",
title = "A note on the efficient implementation of certain
{Pad}{\'e} methods for linear parabolic problems",
journal = j-BIT,
volume = "18",
number = "1",
pages = "106--109",
month = mar,
year = "1978",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01947749",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65M99",
MRnumber = "488820",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "BIT. Nordisk Tidskrift for Informationsbehandling
(BIT)",
journal-URL = "http://link.springer.com/journal/10543",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Field:1978:EBC,
author = "David A. Field",
title = "Error bounds for continued fractions {$ K(1 / b \sb
{n}) $}",
journal = j-NUM-MATH,
volume = "29",
number = "3",
pages = "261--267",
month = sep,
year = "1978",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01389211",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65E05",
MRnumber = "471272",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Kagiwada:1978:IMI,
author = "H. Kagiwada and R. Kalaba",
title = "Imbedding methods for integral equations with
applications",
journal = j-J-OPT-THEORY-APPL,
volume = "24",
number = "1",
pages = "29--57",
year = "1978",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/BF00933181",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "65R05 (45B05)",
MRnumber = "488906",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
note = "Issue devoted to numerical methods for solving
integral equations",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Rall:1978:RKG,
author = "L. B. Rall",
title = "Resolvent kernels of {Green}'s function kernels and
other finite-rank modifications of {Fredholm} and
{Volterra} kernels",
journal = j-J-OPT-THEORY-APPL,
volume = "24",
number = "1",
pages = "59--88",
year = "1978",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/BF00933182",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "65R05 (45B05)",
MRnumber = "488912",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
note = "Issue devoted to numerical methods for solving
integral equations",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Schiop:1978:APR,
author = "A. I. {\c{S}}chiop",
title = "An alternative proof of a result of {Lees}",
journal = "Universit{\v{a}}{\c{t}}ii din Craiova. Analele.
Matematic{\u{a}}, Fizic{\u{a}}-Chimie",
volume = "6",
pages = "43--45",
year = "1978",
MRclass = "65L10",
MRnumber = "601831",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "An. Univ. Craiova Mat. Fiz.-Chim.",
fjournal = "Universit{\v{a}}{\c{t}}ii din Craiova. Analele.
Matematic{\u{a}}, Fizic{\u{a}}-Chimie",
remark = "No online archives, and no ISSN or DOI values.",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Schonfelder:1978:CEE,
author = "J. L. Schonfelder",
title = "{Chebyshev} expansions for the error and related
functions",
journal = j-MATH-COMPUT,
volume = "32",
number = "144",
pages = "1232--1240",
month = oct,
year = "1978",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2006347",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D20 (33A20)",
MRnumber = "494846",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Brezinski:1980:GEA,
author = "C. Brezinski",
title = "A general extrapolation algorithm",
journal = j-NUM-MATH,
volume = "35",
number = "2",
pages = "175--187",
month = jun,
year = "1980",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01396314",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65B05",
MRnumber = "81j:65015 (585245)",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
classification = "C4130 (Interpolation and function approximation)",
corpsource = "UER IEEA, Univ. de Lille 1, Villeneuve d'Ascq,
France",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "convergence acceleration; extrapolation; extrapolation
algorithm; linear extrapolation; rational
extrapolation; recursive algorithm; sequence
transformations",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
treatment = "T Theoretical or Mathematical",
}
@Article{Christiansen:1980:DCU,
author = "J. Christiansen and R. D. Russell",
title = "Deferred corrections using uncentered end formulas",
journal = j-NUM-MATH,
volume = "35",
number = "1",
pages = "21--33",
month = mar,
year = "1980",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01396367",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65B05 (65L10)",
MRnumber = "82e:65006 (583653)",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
classification = "C4130 (Interpolation and function approximation)",
corpsource = "Dept. of Math., Simon Fraser Univ., Burnaby, BC,
Canada",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "approximation theory; asymptotic expansion;
discretization method; Fox difference corrections;
trapezoidal rule; truncation error; uncentered end
formula",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
treatment = "T Theoretical or Mathematical",
}
@Article{Dougalis:1980:SGA,
author = "Vassilios A. Dougalis and Steven M. Serbin",
title = "On the superconvergence of {Galerkin} approximations
to second-order hyperbolic equations",
journal = j-SIAM-J-NUMER-ANAL,
volume = "17",
number = "3",
pages = "431--446",
month = jun,
year = "1980",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0717037",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65M99",
MRnumber = "81j:65106 (581490)",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Glowinski:1980:EPS,
author = "R. Glowinski and J. Periaux and O. Pironneau",
title = "An efficient preconditioning scheme for iterative
numerical solutions of partial differential equations",
journal = j-APPL-MATH-MODEL,
volume = "4",
number = "3",
pages = "187--192",
month = jun,
year = "1980",
CODEN = "AMMODL",
DOI = "https://doi.org/10.1016/0307-904X(80)90130-4",
ISSN = "0307-904x (print), 1872-8480 (electronic)",
ISSN-L = "0307-904X",
MRclass = "65Nxx (65F10)",
MRnumber = "574068",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "Appl. Math. Modelling",
fjournal = "Applied Mathematical Modelling",
journal-URL = "https://www.sciencedirect.com/journal/applied-mathematical-modelling",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Longsine:1980:SRQ,
author = "D. E. Longsine and S. F. McCormick",
title = "Simultaneous {Rayleigh}-quotient minimization methods
for {$ A x = \lambda B x $}",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "34",
number = "??",
pages = "195--234",
month = dec,
year = "1980",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(80)90166-4",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15 (15A18 65N99)",
MRnumber = "82b:65022 (591432)",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/linala1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0024379580901664",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
keywords = "nla, geig, Rayleigh quotient, simultaneous iteration",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Paige:1980:AEL,
author = "C. C. Paige",
title = "Accuracy and Effectiveness of the {Lanczos} Algorithm
for the Symmetric Eigenproblem",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "34",
number = "??",
pages = "235--258",
month = dec,
year = "1980",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(80)90167-6",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15 (15A18 15A57 65N99)",
MRnumber = "82b:65025 (591433)",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/linala1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0024379580901676",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
keywords = "nla, eig, Lanczos algorithm, rounding error",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Zadunaisky:1980:IIA,
author = "P. E. Zadunaisky and G. Lafferriere",
title = "On an iterative improvement of the approximate
solution of some ordinary differential equations",
journal = j-COMPUT-MATH-APPL,
volume = "6",
number = "1",
pages = "147--154",
year = "1980",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(80)90066-8",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "65L99 (34A50)",
MRnumber = "604091",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Computers \& Mathematics with Applications. An
International Journal",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Munz:1981:UEC,
author = "Harry Munz",
title = "Uniform expansions for a class of finite difference
schemes for elliptic boundary value problems",
journal = j-MATH-COMPUT,
volume = "36",
number = "153",
pages = "155--170",
month = jan,
year = "1981",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1981-0595048-7;
https://doi.org/10.2307/2007732",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65N05",
MRnumber = "82b:65098 (595048)",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "C4170 (Differential equations); C4180 (Integral
equations)",
corpsource = "Inst. fur Biologie, Tubingen, West Germany",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "approximate solution; boundary-value problems;
Dirichlet problem; elliptic boundary value problems;
error bounds; finite difference schemes",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
treatment = "T Theoretical or Mathematical",
}
@Article{Ortiz:1981:OAT,
author = "E. L. Ortiz and H. Samara",
title = "An operational approach to the tau method for the
numerical solution of nonlinear differential
equations",
journal = j-COMPUTING,
volume = "27",
number = "1",
pages = "15--25",
month = mar,
year = "1981",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/BF02243435",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65L10",
MRnumber = "83b:65079 (623173)",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
affiliation = "Univ of London, Engl",
classification = "921",
fjournal = "Computing. Archives for Scientific Computing",
journal-URL = "https://link.springer.com/journal/607/volumes-and-issues",
journalabr = "Computing (Vienna/New York)",
keywords = "mathematical techniques",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Shintani:1981:PRK,
author = "Hisayoshi Shintani",
title = "On pseudo-{Runge--Kutta} methods of the third kind",
journal = "Hiroshima Mathematical Journal",
volume = "11",
number = "2",
pages = "247--254",
month = jul,
year = "1981",
DOI = "https://doi.org/10.32917/hmj/1206134099",
ISSN = "0018-2079",
ISSN-L = "0018-2079",
MRclass = "65L05",
MRnumber = "620536",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
URL = "http://projecteuclid.org/euclid.hmj/1206134099",
acknowledgement = ack-nhfb,
ajournal = "Hiroshima Math. J.",
fjournal = "Hiroshima Mathematical Journal",
journal-URL = "https://projecteuclid.org/journals/hiroshima-mathematical-journal",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Takahasi:1981:PCG,
author = "Hidetosi Takahasi and Takashi Nodera",
title = "Preconditioned conjugate gradient algorithms for
nonsymmetric matrix",
journal = "Keio Mathematical Seminar Reports",
number = "6",
pages = "51--70",
year = "1981",
ISSN = "0388-3469",
ISSN-L = "0388-3469",
MRclass = "65F30",
MRnumber = "628393",
MRreviewer = "L. Fox",
bibdate = "Tue Nov 14 17:19:58 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "Keio Math. Sem. Rep.",
fjournal = "Keio Mathematical Seminar Reports",
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Anonymous:1952:TCP,
editor = "Anonymous",
booktitle = "Tables of {Chebyshev} polynomials, {$ S_n(x) $} and {$
C_n(x) $}",
title = "Tables of {Chebyshev} polynomials, {$ S_n(x) $} and {$
C_n(x) $}",
volume = "9",
publisher = pub-USGPO,
address = pub-USGPO:adr,
pages = "xxx + 161",
year = "1952",
LCCN = "????",
MRclass = "65.0X",
MRnumber = "68893",
MRreviewer = "L. Fox",
bibdate = "Wed Jun 08 18:57:59 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Foreword by J. C. P. Miller. Introduction by Cornelius
Lanczos.",
series = "National Bureau of Standards Applied Mathematics
Series",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Miller:1949:CMT,
author = "J. C. P. Miller",
title = "The construction of mathematical tables",
journal = "The scientific journal of the Royal College of
Science",
volume = "20",
number = "??",
pages = "1--11",
month = "????",
year = "1949",
CODEN = "SJRCAE",
ISSN = "0371-0467",
ISSN-L = "0371-0467",
bibdate = "Tue Nov 14 15:15:39 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "Sci. J. R. Coll. Sci.",
fjournal = "The scientific journal of the Royal College of
Science",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Tocher:1955:BRBc,
author = "K. D. Tocher",
title = "Book Review: {{\booktitle{A Short Table for Bessel
Functions of Integer Orders and Large Arguments}}, by
L. Fox; \booktitle{Table of Binomial Coefficients}, by
J. C. P. Miller}",
journal = j-J-R-STAT-SOC-SER-A-GENERAL,
volume = "118",
number = "1",
pages = "106--107",
month = "????",
year = "1955",
CODEN = "JSSAEF",
DOI = "https://doi.org/10.2307/2342530",
ISSN = "0035-9238",
ISSN-L = "0035-9238",
bibdate = "Sat Jan 24 11:18:11 MST 2015",
bibsource = "http://www.jstor.org/stable/i315902;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/jrss-a-1950.bib",
URL = "http://www.jstor.org/stable/2342530",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society. Series A
(General)",
journal-URL = "http://www.jstor.org/journals/00359238.html",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Selfridge:1958:RPN,
author = "R. G. Selfridge",
title = "Recent Publications: {{\em The Numerical Solution of
Two-Point Boundary Problems in Ordinary Differential
Equations}}, by {L. Fox}",
journal = j-AMER-MATH-MONTHLY,
volume = "65",
number = "8",
pages = "641--642",
month = oct,
year = "1958",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2309147",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Fri Jul 9 10:29:48 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/amermathmonthly1955.bib",
URL = "https://www.jstor.org/stable/2309147",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Henrici:1959:BRN,
author = "Peter Henrici",
title = "Book Review: {{\booktitle{The Numerical Solution of
Two-Point Boundary Problems in Ordinary Differential
Equations}}, by L. Fox}",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "13",
number = "68",
pages = "322--323",
month = oct,
year = "1959",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.2307/2002815",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Mon Jan 28 11:08:53 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib",
URL = "https://www.jstor.org/stable/2002815",
acknowledgement = ack-nhfb,
author-dates = "Peter Karl Henrici (13 September 1923--13 March
1987)",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Thompson:1959:BRN,
author = "G. T. Thompson",
title = "Book Review: {{\booktitle{The Numerical Solution of
Two-Point Boundary Problems in Ordinary Differential
Equations}} By L. Fox. Oxford University Press, New
York, 1957. xi + 371 pp.}",
journal = j-SIAM-REVIEW,
volume = "1",
number = "2",
pages = "177--178",
month = jul,
year = "1959",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1001035",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:04:26 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/1/2;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "July 1959",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Todd:1959:BRF,
author = "John Todd",
title = "Book Review: {L. Fox. \booktitle{The use and
construction of mathematical tables}. National Physical
Lab., Math. Tables, v. 1, Her Majesty's Stationery
Office, London, England, 1956, 60 p., 27.5 cm.}",
journal = j-MATH-COMPUT,
volume = "13",
number = "65",
pages = "61--64",
month = jan,
year = "1959",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2002204",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Mon Oct 23 08:09:13 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib",
URL = "https://www.jstor.org/stable/2002204",
acknowledgement = ack-nhfb,
author-dates = "John Todd (16 May 1911--21 June 2007)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{L:1961:BRF,
author = "Y. L. L.",
title = "Book Review: {L. Fox, \booktitle{Tables of Weber
Parabolic Cylinder Functions and Other Functions for
Large Arguments}, National Physical Laboratory
Mathematical Tables Volume 4, Her Majesty's Stationery
Office, London, 1960, iii + 40 p., 28 cm.
(Paperback)}",
journal = j-MATH-COMPUT,
volume = "15",
number = "75",
pages = "310--311",
month = jul,
year = "1961",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-61-99215-8",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Wed Nov 15 11:07:36 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
URL = "http://www.jstor.org/stable/2002928;
https://www.ams.org/journals/mcom/1961-15-075/S0025-5718-61-99215-8/S0025-5718-61-99215-8.pdf",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Y. L. L. == Yudell L. Luke",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{P:1964:BRF,
author = "H. P.",
title = "Book Review: {L. Fox, \booktitle{Numerical Solution of
Ordinary and Partial Differential Equations},
Addison-Wesley Publishing Company, Inc., Reading,
Mass., 1962, ix + 509 p., 23.5 cm.}",
journal = j-MATH-COMPUT,
volume = "18",
number = "87",
pages = "528--528",
month = jul,
year = "1964",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-64-99162-8",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Wed Nov 15 14:55:23 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
URL = "http://www.jstor.org/stable/2003801",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "H. P. == H. Pollard",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Pollard:1964:RPPa,
author = "H. Pollard",
title = "Recent Publications and Presentations:
{{\booktitle{Numerical Solution of Ordinary and Partial
Differential Equations}}, by L. Fox}",
journal = j-AMER-MATH-MONTHLY,
volume = "71",
number = "8",
pages = "938--938",
month = oct,
year = "1964",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2312444",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:37:37 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/amermathmonthly1960.bib",
URL = "https://www.jstor.org/stable/2312444",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Todd:1964:BRN,
author = "John Todd",
title = "Book Review: {{\booktitle{Numerical Solution of
Ordinary and Partial Differential Equations}} edited by
L. Fox, 509 pages; Addison-Wesley Publishing Co.,
1962}",
journal = j-AM-SCI,
volume = "52",
number = "1",
pages = "116A-117A",
month = mar,
year = "1964",
CODEN = "AMSCAC",
ISSN = "0003-0996 (print), 1545-2786 (electronic)",
ISSN-L = "0003-0996",
bibdate = "Mon Oct 23 08:09:13 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib",
URL = "https://www.jstor.org/stable/27838969",
acknowledgement = ack-nhfb,
author-dates = "John Todd (16 May 1911--21 June 2007)",
fjournal = "American Scientist",
journal-URL = "http://www.americanscientist.org/issues/past.aspx",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Baker:1966:BRI,
author = "Christopher T. H. Baker",
title = "Book Review: {{\booktitle{An Introduction to Numerical
Linear Algebra with Exercises}}. By L. Fox. Oxford
University Press, New York, 1965. xi + 327 pp.}",
journal = j-SIAM-REVIEW,
volume = "8",
number = "1",
pages = "125--127",
month = jan,
year = "1966",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1008031",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:05:31 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/8/1;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1966",
remark = "From the first two paragraphs: ``This book is second
in a series of Monographs on Numerical Analysis. It
succeeds \booktitle{The Numerical Solution of Two-point
Boundary Problems in Ordinary Differential Equations},
written by the same author in 1957, nd is being
followed by \booktitle{The Algebraic Eigenvalue
Problem} by J. H. Wilkinson. But for the inclusion of
exercises, the book under review is essentially
identical to the first British edition, \booktitle{An
Introduction to Numerical Linear Algebra}, published in
1964 by the Clarendon Press, Oxford, England.''",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Bueckner:1966:RPD,
author = "Hans F. Bueckner",
title = "Remark on a Paper by {D. S. Griffin} and {R. S. Varga}
{``Numerical Solution of Plane Elasticity Problems''
[J. SIAM {\bf 11} (1963), no. 4, 1046--1062]}",
journal = j-SIAM-J-APPL-MATH,
volume = "14",
number = "2",
pages = "414--414",
month = mar,
year = "1966",
CODEN = "SMJMAP",
DOI = "https://doi.org/10.1137/01140",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib;
https://www.math.utah.edu/pub/tex/bib/siam.bib;
https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
JSTOR database",
note = "See \cite{Griffin:1963:NSP} and comment
\cite{Griffin:1966:CBR}.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
subject-dates = "Richard S. Varga (8 October 1928--25 February 2022)",
}
@Article{Griffin:1966:CBR,
author = "D. S. Griffin and R. S. Varga",
title = "Comments on {Bueckner's Remark on a Paper by D. S.
Griffin and R. S. Varga}",
journal = j-SIAM-J-APPL-MATH,
volume = "14",
number = "2",
pages = "415--416",
month = mar,
year = "1966",
CODEN = "SMJMAP",
DOI = "https://doi.org/10.1137/0114034",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Wed Nov 15 10:13:39 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib",
note = "See \cite{Griffin:1963:NSP,Bueckner:1966:RPD}.",
acknowledgement = ack-nhfb,
author-dates = "Richard S. Varga (8 October 1928--25 February 2022)",
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
}
@Article{Burstall:1967:BRA,
author = "R. M. Burstall",
title = "Book Review: {{\booktitle{Advances in Programming and
Non-Numerical Computation}}. Edited by L. Fox. 63s.
1966. (Pergamon)}",
journal = j-MATH-GAZ,
volume = "51",
number = "377",
pages = "277--278",
month = oct,
year = "1967",
CODEN = "MAGAAS",
ISSN = "0025-5572 (print), 2056-6328 (electronic)",
ISSN-L = "0025-5572",
bibdate = "Wed Nov 15 15:01:32 2023",
URL = "http://www.jstor.org/stable/3613292",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Gazette",
journal-URL = "http://www.jstor.org/journal/mathgaze",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
}
@Article{Gunzenhauser:1967:BRA,
author = "R. Gunzenh{\"a}user",
title = "Book Report: {{\booktitle{Advances in Programming and
Non-Numerical Computations}}, Herausgegeben von L. Fox.
viii, 218 S. Oxford-London-Edinburgh-New
York-Paris-Frankfurt: Pergamon Press. 1966}",
journal = j-COMPUTING,
volume = "2",
number = "2",
pages = "180--180",
month = jun,
year = "1967",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/BF02239186",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Wed Nov 15 17:04:26 2000",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/computing.bib",
acknowledgement = ack-ec,
fjournal = "Computing",
journal-URL = "https://link.springer.com/journal/607/volumes-and-issues",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{McGee:1967:BRA,
author = "William C. McGee",
title = "Book Review: {{\booktitle{Advances in Programming \&
Non-Numerical Computation}} Edited by L. Fox. Pergamon
Press, Inc., New York, 1966. viii + 218 pp.}",
journal = j-SIAM-REVIEW,
volume = "9",
number = "1",
pages = "133--136",
month = jan,
year = "1967",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1009022",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:05:42 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/9/1;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1967",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Clenshaw:1968:BRC,
author = "C. W. Clenshaw",
title = "Book Review: {{\booktitle{Chebyshev Polynomials in
Numerical Analysis}}, by L. Fox and I. B. Parker, 1969;
205 pages (Oxford University Press)}",
journal = j-COMP-J,
volume = "11",
number = "3",
pages = "310--310",
month = mar,
year = "1968",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/11.3.310",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:41 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/11/3.toc;
https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/compj1960.bib",
URL = "http://comjnl.oxfordjournals.org/content/11/3/310.full.pdf+html",
acknowledgement = ack-nhfb,
author-dates = "Charles William Clenshaw (15 March 1926--23 September
2004)",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Baer:1969:RCM,
author = "R. M. Baer",
title = "Reviews: {{\em Computing Methods for Scientists and
Engineers}}, by {L. Fox and D. F. Mayers}",
journal = j-AMER-MATH-MONTHLY,
volume = "76",
number = "10",
pages = "1163--1163",
month = dec,
year = "1969",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2317225",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:39:36 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/amermathmonthly1965.bib",
URL = "https://www.jstor.org/stable/2317225",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Todd:1975:CLC,
author = "John Todd",
title = "Corrigendum: {``The Lemniscate Constants''}",
journal = j-CACM,
volume = "18",
number = "8",
pages = "462--462",
month = aug,
year = "1975",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/360933.360984",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Dec 26 18:42:09 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib",
note = "See \cite{Todd:1975:LC}.",
acknowledgement = ack-nhfb,
author-dates = "John Todd (16 May 1911--21 June 2007)",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Anonymous:1985:FPC,
author = "Anonymous",
title = "{1985 L. Fox} Prize: Call for Entries",
journal = j-IMA-J-NUMER-ANAL,
volume = "5",
number = "1",
pages = "1--1",
month = jan,
year = "1985",
CODEN = "IJNADH",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65L05",
MRnumber = "86f:65114",
MRreviewer = "G. Hall",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
remark = "Article lost at publisher Web site.",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{McClamroch:1985:BRG,
author = "N. Harris McClamroch",
title = "Book Review: {{\booktitle{A Guide to Simulation}}. By
Paul Bratley, Bennett L. Fox, and Linus E. Schrage.
Springer-Verlag, New York, 1.983. xviv + 383 pp. ISBN
0-387-90820-X}",
journal = j-SIAM-REVIEW,
volume = "27",
number = "2",
pages = "292--293",
month = jun,
year = "1985",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1027092",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:53:55 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/27/2;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "June 1985",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Kershaw:1987:AMF,
author = "D. Kershaw",
title = "An analysis of the method of {L. Fox} and {L. Hayes}
for the factorization of a polynomial",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "86",
number = "??",
pages = "179--187",
month = feb,
year = "1987",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(87)90293-X",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "12D05 (11Y05 15A23 26C10 65H05)",
MRnumber = "88a:12001",
MRreviewer = "Thomas H. Foregger",
bibdate = "Wed Nov 30 13:50:22 MST 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/linala1980.bib",
note = "See \cite{Fox:1968:PFQ}.",
URL = "http://www.sciencedirect.com/science/article/pii/002437958790293X",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Booklet{Anonymous:1992:LF,
author = "Anonymous",
title = "{Leslie Fox: 1918--1992}",
howpublished = "Oxford University booklet.",
pages = "ii + 77",
year = "1992",
bibdate = "Sun Nov 12 09:43:02 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
note = "Includes brief curriculum vitae (completed 3 days
before Leslie Fox's death), and a bibliography of his
publications. Memories of Leslie Fox by C. W. Clenshaw,
pp. 7--10.",
URL = "https://people.maths.ox.ac.uk/wathen/fox/Leslie_Fox_booklet_1994.pdf",
acknowledgement = ack-nhfb,
keywords = "A. R. Curtis; A. R. Davies; Brian Ford; D. C.
Hanscomb; D. Higham; D. Kershaw; Frank W. J. Olver;
Gene Golub; Gilbert Strang; Iain Duff; J. Du Croz; J.
Lyness; James Demmel; John Ker Reid; M. Powell; Nick I.
M. Gould; P. Davies; Peter Monk; Sven Hammaring",
subject-dates = "Charles William Clenshaw (15 March 1926--23 September
2004); Leslie Fox (1918--1 August 1992)",
}
@Article{Clenshaw:1992:OPL,
author = "Charles Clenshaw",
title = "Obituary: {Professor Leslie Fox}",
journal = "The Independent",
volume = "??",
number = "??",
pages = "??--??",
day = "10",
month = aug,
year = "1992",
bibdate = "Wed Nov 15 07:51:22 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
URL = "https://www.independent.co.uk/news/people/obituary-professor-leslie-fox-1539620.html",
acknowledgement = ack-nhfb,
remark = "From the article: ``Fox argued consistently for
adherence to basic principles; in particular he urged
that all computed results should be assumed wrong until
proved otherwise.''",
author-dates = "Charles William Clenshaw (15 March 1926--23 September
2004)",
subject-dates = "Leslie Fox (1918--1 August 1992)",
}
@Article{Duff:1993:ELF,
author = "I. S. Duff and G. A. Watson and others",
title = "Editorial: {Leslie Fox}, 1918--1992",
journal = j-IMA-J-NUMER-ANAL,
volume = "13",
number = "1",
pages = "i--ii",
month = jan,
year = "1993",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/13.1.1",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "01A70",
MRnumber = "1199025",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Nichols:1993:OPL,
author = "Nancy K. Nichols",
title = "Obituary: {Professor Leslie Fox}",
journal = j-BULL-INST-MATH-APPL,
volume = "29",
number = "11--12",
pages = "175--176",
year = "1993",
CODEN = "IMTABW",
ISSN = "0905-5628",
MRclass = "01A70",
MRnumber = "1263575",
bibdate = "Mon Nov 13 14:47:36 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
ajournal = "Bull. Inst. Math. Appl.",
fjournal = "Bulletin of the Institute of Mathematics and its
Applications",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Mayers:1999:OLF,
author = "David F. Mayers and J. E. Walsh",
title = "Obituary: {Leslie Fox}",
journal = j-BULL-LOND-MATH-SOC,
volume = "31",
number = "2",
pages = "241--247",
month = mar,
year = "1999",
CODEN = "LMSBBT",
DOI = "https://doi.org/10.1112/S0024609398004950",
ISSN = "0024-6093 (print), 1469-2120 (electronic)",
ISSN-L = "0024-6093",
MRclass = "01A70",
MRnumber = "1664141",
bibdate = "Mon Nov 13 14:47:36 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "The Bulletin of the London Mathematical Society",
journal-URL = "http://blms.oxfordjournals.org/content/by/year",
remark = "This memoir contains a list of 90 publications by
Leslie Fox.",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{McKee:2018:MRP,
author = "Sean McKee",
title = "My recollections of {Professor Leslie Fox}",
journal = j-MATH-TODAY,
volume = "54",
number = "4",
pages = "148",
year = "2018",
ISSN = "1361-2042",
ISSN-L = "1361-2042",
MRclass = "01A70",
MRnumber = "3837606",
bibdate = "Mon Nov 13 14:47:36 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics Today",
journal-URL = "http://ima.org.uk/activities/publications/mathematics_today.cfm.html",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Ockendon:2018:LFO,
author = "John Ockendon and Andy Wathen",
title = "{Leslie Fox} and {Oxford}",
journal = j-MATH-TODAY,
volume = "54",
number = "4",
pages = "146--147",
year = "2018",
ISSN = "1361-2042",
ISSN-L = "1361-2042",
MRclass = "01A70",
MRnumber = "3837605",
bibdate = "Mon Nov 13 14:47:36 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics Today",
journal-URL = "http://ima.org.uk/activities/publications/mathematics_today.cfm.html",
subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Article{Richardson:1911:IAA,
author = "Lewis Fry Richardson",
title = "{IX}. {The} approximate arithmetical solution by
finite differences of physical problems involving
differential equations with an application to the
stresses in a masonry dam",
journal = j-PHILOS-TRANS-R-SOC-LOND-SER-A,
volume = "A210",
number = "459--470",
pages = "307--357",
day = "1",
month = jan,
year = "1911",
CODEN = "PTRMAD, PTMSFB",
DOI = "https://doi.org/10.1098/rsta.1911.0009",
ISSN = "1364-503X (print), 1471-2962 (electronic)",
ISSN-L = "1364-503X",
bibdate = "Sun Oct 29 07:04:54 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
URL = "https://royalsocietypublishing.org/doi/10.1098/rsta.1911.0009",
acknowledgement = ack-nhfb,
fjournal = "Philosophical Transactions of the Royal Society A:
Mathematical, Physical, and Engineering Sciences",
journal-URL = "http://rsta.royalsocietypublishing.org/",
}
@Article{Bickley:1936:LNS,
author = "W. G. Bickley and J. C. P. Miller",
title = "{LX}. {The} numerical summation of slowly convergent
series of positive terms",
journal = j-PHILOS-MAG,
volume = "22",
number = "149",
pages = "754--767",
month = nov,
year = "1936",
CODEN = "PHMAA4",
DOI = "https://doi.org/10.1080/14786443608561726",
ISSN = "0031-8086",
ISSN-L = "0031-8086",
bibdate = "Tue Nov 14 14:47:51 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/tex/bib/convacc.bib",
URL = "https://www.tandfonline.com/doi/abs/10.1080/14786443608561726",
acknowledgement = ack-nhfb,
fjournal = "Philosophical Magazine",
journal-URL = "http://www.tandfonline.com/loi/tphm19",
keywords = "convergence acceleration",
}
@Book{Anonymous:1952:BFP,
author = "Anonymous",
title = "{Bessel} Functions, {Part II}",
volume = "10",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "????",
year = "1952",
bibdate = "Tue Nov 14 14:59:31 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
series = "British Association Mathematical Tables",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
remark = "TO DO: was Leslie Fox a co-author?? Who were the
authors?? Page count??",
}
@InCollection{Todd:2000:LC,
author = "John Todd",
title = "The Lemniscate Constants",
crossref = "Berggren:2000:PSB",
pages = "412--417",
year = "2000",
DOI = "https://doi.org/10.1007/978-1-4757-3240-5_45",
bibdate = "Mon Oct 23 08:09:13 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib",
note = "Reprint of \cite{Todd:1975:LC}",
acknowledgement = ack-nhfb,
author-dates = "John Todd (16 May 1911--21 June 2007)",
}
@Book{Langer:1959:NAP,
editor = "R. E. Langer",
booktitle = "On Numerical Approximation. {Proceedings of a
Symposium, Madison, April 21--23, 1958}",
title = "On Numerical Approximation. {Proceedings of a
Symposium, Madison, April 21--23, 1958}",
publisher = "The University of Wisconsin Press",
address = "Madison, WI, USA",
pages = "x + 462",
year = "1959",
LCCN = "QA3 .U45 no. 1",
bibdate = "Tue Jun 19 06:45:47 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "Publication no. 1 of the Mathematics Research Center,
U.S. Army, the University of Wisconsin.",
acknowledgement = ack-nhfb,
subjects = "statistics",
tableofcontents = "1. On trends and problems in numerical
approximation / Ostrowski \\
2. Linear spaces and approximation theory / Buck \\
3. Operational methods in numerical analysis based on
rational approximations / Kopal \\
4. On the numerical integration of periodic analytic
functions / Davis \\
S. Some new divided difference algorithms in two
variables / Salzer \\
6. Numerical evaluation of multiple integrals / Hammer
\\
7. Optimal approximation and error bounds / Golomb and
Weinberger \\
8. The rationale of approximation / Sard \\
9. On extremal approximations / Walsh \\
10. Numerical methods of Tchebycheff approximation /
Stiefel \\
11. Minimax methods in table construction / Fox \\
12. Existence of essentially nonlinear families
suitable for oscillatory approximation / Motzkin \\
13. On variation diminishing approximation methods /
Schoenberg \\
14. Approximation by functions of fewer variables /
Golomb \\
15. Extremal approximations --- a summary / Miller \\
16. Survey of recent Russian literature on
approximation / Buck \\
17. The quotient--difference and epsilon algorithms /
Bauer \\
18. Some sufficient conditions for the existence of an
asymptotic formula or an asymptotic expansion / Rosser
\\
19. The estimation of (power) spectra and related
quantities / Tukey \\
20. Approximation in partial differential equations /
Collatz \\
21. Special polynomials in numerical analysis / Todd",
}
@Book{Fox:1962:NSO,
editor = "L. Fox",
booktitle = "Numerical Solution of Ordinary and Partial
Differential Equations. {Based} on a Summer School Held
in {Oxford, August--September 1961}",
title = "Numerical Solution of Ordinary and Partial
Differential Equations. {Based} on a Summer School Held
in {Oxford, August--September 1961}",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "509",
year = "1962",
LCCN = "QA371 .L758 1962",
bibdate = "Tue Nov 14 06:49:23 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Fox:1966:APN,
editor = "L. Fox",
booktitle = "Advances in Programming and Non-numerical
Computation",
title = "Advances in Programming and Non-Numerical
Computation",
volume = "3",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "viii + 218",
year = "1966",
LCCN = "QA76 .F64 1966",
bibdate = "Tue Nov 14 07:06:55 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
series = "Proceedings of summer schools organised by the Oxford
University Computing Laboratory and the Delegacy for
Extra-mural Studies",
acknowledgement = ack-nhfb,
author-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Book{Walsh:1966:NAI,
editor = "Joan E. Walsh",
booktitle = "Numerical Analysis, an Introduction. {Based} on a
symposium organized by the {Institute of Mathematics
and Its Applications, Birmingham, England, 1965}",
title = "Numerical Analysis, an Introduction. {Based} on a
symposium organized by the {Institute of Mathematics
and Its Applications, Birmingham, England, 1965}",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xiv + 212",
year = "1966",
LCCN = "QA297 .N84 1967",
bibdate = "Tue Nov 14 08:45:24 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Dejon:1969:CAF,
editor = "Bruno Dejon and Peter Henrici",
booktitle = "Constructive Aspects of the Fundamental Theorem of
Algebra: proceedings of a symposium conducted at the
{IBM Research Laboratory, Z{\"u}rich-R{\"u}schlikon,
Switzerland, June 5--7, 1967}",
title = "Constructive Aspects of the Fundamental Theorem of
Algebra: proceedings of a symposium conducted at the
{IBM Research Laboratory, Z{\"u}rich-R{\"u}schlikon,
Switzerland, June 5--7, 1967}",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "337",
year = "1969",
ISBN = "0-471-20300-9",
ISBN-13 = "978-0-471-20300-1",
LCCN = "QA212 .C65",
bibdate = "Sun Jan 27 19:57:13 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/householder-alston-s.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib",
ZMnumber = "0175.00104",
acknowledgement = ack-nhfb,
author-dates = "Peter Karl Henrici (13 September 1923--13 March
1987)",
subject = "Equations, Roots of; Congresses; Fundamental theorem
of algebra; Congresses",
tableofcontents = "A never failing, fast convergent root-finding
algorithm / B. Dejon and K. Nickel \\
Finding a zero by means of successive linear
interpolation / T. J. Dekker \\
Remarks on the paper by Dekker / G. E. Forsythe \\
What is a satisfactory quadratic equation solver? / G.
E. Forsythe \\
Mathematical and physical polynomials / L. Fox \\
A constructive form of the second Gauss proof of the
Fundamental Theorem of Algebra / R. L. Goodstein \\
Uniformly convergent algorithms for the simultaneous
approximation of all zeros of a polynomial / P. Henrici
and I. Gargantini \\
On the notion of constructivity / H. Hermes \\
Bigradients, Hankel determinants, and the Pad{\'e}
table / A. S. Householder and G. W. Stewart \\
An algorithm for an automatic general polynomial solver
/ M. A. Jenkins and J. F. Traub \\
Die numerische Bestimmung mehrfacher und nahe
benachbarter polynomnullstellen nach einem verbesserten
Bernoulli-Verfahren / I. Kupka \\
Search procedures for polynomial equation solving / D.
H. Lehmer \\
A method for automatic solution of algebraic equations
/ A. M. Ostrowski \\
Iteration functions for solving polynomial matrix
equations / M. Pavel-Parvu and A. Korganoff \\
Problematik der Nullstellenbestimmung bei polynomen /
H. Rutishauser \\
Factorization of polynomials by generalized Newton
procedures / J. Schroder \\
The fundamental theorem of algebra in recursive
analysis / E. Specker",
}
@Proceedings{Jacobs:1977:SAN,
editor = "David A. H. Jacobs",
booktitle = "{The State of the Art in Numerical Analysis:
Proceedings of the Conference on the State of the Art
in Numerical Analysis held at the University of York,
April 12th--15th, 1976}",
title = "{The State of the Art in Numerical Analysis:
Proceedings of the Conference on the State of the Art
in Numerical Analysis held at the University of York,
April 12th--15th, 1976}",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xix + 978",
year = "1977",
ISBN = "0-12-378650-9",
ISBN-13 = "978-0-12-378650-0",
LCCN = "QA297 .C646 1976",
bibdate = "Tue Mar 20 14:45:09 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
meetingname = "Conference on the State of the Art in Numerical
Analysis, York, Eng., 1976.",
subject = "Numerical analysis; Congresses",
xxbooktitle = "The state of the art in numerical analysis
({Proceedings of the Conference, University of York,
Heslington, 1976})",
}
@Proceedings{Crane:1987:HAC,
editor = "G. E. Crane",
booktitle = "{HSNC'87: ACM Conference on the History of Scientific
and Numeric Computation, conference proceedings: papers
presented at the Conference, Princeton, New Jersey, May
13-15, 1987}",
title = "{HSNC'87: ACM Conference on the History of Scientific
and Numeric Computation, conference proceedings: papers
presented at the Conference, Princeton, New Jersey, May
13-15, 1987}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "viii + 150",
month = oct,
year = "1987",
ISBN = "0-89791-229-2",
ISBN-13 = "978-0-89791-229-7",
LCCN = "QA76 .A25 1987",
bibdate = "Tue Nov 14 13:59:59 MST 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://portal.acm.org/proceedings/hsnc/;
https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/gear-c-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib",
acknowledgement = ack-nhfb,
author-dates = "David M. Young, Jr. (October 20, 1923--December 21,
2008); George Elmer Forsythe (8 January 1917--9 April
1972); John Todd (16 May 1911--21 June 2007); John W.
Tukey (16 June 1915--26 July 2000); Leslie Fox (30
September 1918--1 August 1992); Magnus Rudolph Hestenes
(13 February 1906--31 May 1991)",
remark = "Sponsored by the Allegheny Region of the Association
for Computing Machinery in cooperation with ACM SIGNUM
and the Society for Industrial and Applied
Mathematics.",
subject = "Electronic data processing; Congresses; Electronic
digital computers; Ordinateurs; Congr{\`e}s; Electronic
data processing.; Electronic digital computers.",
subject-dates = "George Elmer Forsythe (8 January 1917--9 April 1972);
James H. Wilkinson (27 September 1919--5 October 1986);
John W. Tukey (16 June 1915--26 July 2000)",
tableofcontents = "H. H. Goldstine / Keynote address --- Remembrance
of things past / https://doi.org/10.1145/41579.41580 /
1--16 \\
L. Fox / Early numerical analysis in the United Kingdom
/ https://doi.org/10.1145/41579.41581 / 21--39 \\
J. Todd / The prehistory and ancient history of
computation at the U.S. National Bureau of Standards /
https://doi.org/10.1145/41579.41582 / 47--51 \\
D. J. Wheeler / Programmed computing at the
Universities of Cambridge and Illinois in the early
fifties / https://doi.org/10.1145/41579.41583 / 53--58
\\
The development of methods of using computers for
calculations in the early fifties at Cambridge and
Illinois Universities. They are the recollections of a
participant. \\
J. R. Rice / Mathematical software and ACM Publications
/ https://doi.org/10.1145/41579.41584 / 59--62 \\
M. Gutknecht / The pioneer days of scientific computing
in Switzerland / https://doi.org/10.1145/41579.41585 /
63--69 \\
M. R. Hestenes / Conjugacy and gradients in variational
theory and analysis /
https://doi.org/10.1145/41579.41586 / 71--90 \\
C.-E. Fr{\"o}berg / {B I T} --- a child of the computer
/ https://doi.org/10.1145/41579.41587 / 91--93 \\
I. Babuska / Comments on postwar development of
computational mathematics in some countries of Eastern
Europe / https://doi.org/10.1145/41579.41588 / 95--96
\\
J. W. Cooley / How the FFT gained acceptance /
https://doi.org/10.1145/41579.41589 / 97--100 \\
C. W. Gear, R. Skeel / The development of ODE methods:
a symbiosis between hardware and numerical analysis /
https://doi.org/10.1145/41579.41590 / 105--115 \\
D. M. Young / An historical review of iterative methods
/ https://doi.org/10.1145/41579.41591 / 117--123 \\
T. Oden / Some historic comments on finite elements /
https://doi.org/10.1145/41579.41592 / 125--130 \\
B. N. Parlett / J. H. Wilkinson's work and influence on
matrix computations /
https://doi.org/10.1145/41579.41593 / 133--138 \\
J. Varah / The work of George Forsythe and his students
/ https://doi.org/10.1145/41579.41594 / 139--150",
}
@Proceedings{Cox:1990:RNC,
editor = "M. G. Cox and S. J. Hammarling",
booktitle = "Reliable Numerical Computation",
title = "Reliable Numerical Computation",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xvi + 339",
year = "1990",
ISBN = "0-19-853564-3",
ISBN-13 = "978-0-19-853564-5",
LCCN = "QA297 .R435 1990",
bibdate = "Mon Mar 11 09:29:53 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
price = "US\$45.00",
}
@Book{Nash:1990:HSC,
editor = "Stephen G. Nash",
booktitle = "A History of Scientific Computing",
title = "A History of Scientific Computing",
publisher = pub-AW # " and " # pub-ACM,
address = pub-AW # " and " # pub-ACM:adr,
pages = "xix + 359",
year = "1990",
ISBN = "0-201-50814-1",
ISBN-13 = "978-0-201-50814-7",
LCCN = "QA76.17 .H59 1990",
bibdate = "Wed Dec 15 10:39:57 1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/gear-c-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/householder-alston-s.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;;
https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib;
https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib;
z3950.loc.gov:7090/Voyager",
series = "ACM Press history series",
acknowledgement = ack-nhfb,
author-dates = "Charles William ``Bill'' Gear (1 February 1935--15
March 2022); Garrett Birkhoff (19 January 1911--22
November 1996); Magnus Rudolph Hestenes (13 February
1906--31 May 1991)",
remark = "Based on papers presented at the Conference on the
History of Scientific and Numeric Computation, held in
Princeton, NJ, 1987. A few brief mentions of Alston
Householder are indexed in the book, with photographs
of him on pages xvi and 344.",
subject = "Electronic data processing; History; Science; Data
processing",
tableofcontents = "Remembrance of things past / Herman H. Goldstine /
5--16 \\
The contribution of J. H. Wilkinson to numerical
analysis / B. N. Parlett / 17--30 \\
The influence of George Forsythe and his students /
James Varah / 31--40 \\
Howard H. Aiken and the computer / I. Bernard Cohen /
41--52 \\
Particles in their self-consistent field: from
Hartree's differential analyzer to Cray machines /
Oscar Buneman / 57--62 \\
Fluid dynamics, reactor computations, and surface
representation / Garrett Birkhoff / 63--87 \\
The development of ODE methods: a symbiosis between
hardware and numerical analysis / C. W. Gear and R. D.
Skeel / 88--105 \\
A personal retrospection of reservoir simulation /
Donald W. Peaceman / 106--129 \\
How the FFT gained acceptance / James W. Cooley /
133--140 \\
Origins of the simplex method / George B. Dantzig /
141--151 \\
Historical comments on finite elements / J. Tinsley
Oden / 152--166 \\
Conjugacy and gradients / Magnus R. Hestenes / 167--179
\\
A historical review of iterative methods / David M.
Young / 180--194 \\
Shaping the evolution of numerical analysis in the
computer age: the SIAM thrust / I. Edward Block /
199--205 \\
Reminiscences on the University of Michigan summer
schools, the Gatlinburg Symposia, and Numerische
Mathematik / Richard S. Varga / 206--210 \\
The origin of mathematics of computation and some
personal recollections / Eugene Isaacson / 211--216 \\
Mathematical software and ACM publications / John R.
Rice / 217--227 \\
BIT --- a child of the computer / Carl-Erik Fr{\"o}berg
/ 228--233 \\
The Los Alamos experience, 1943--1954 / N. Metropolis /
237--250 \\
The prehistory and early history of computation at the
U.S. National Bureau of Standards / John Todd /
251--268 \\
Programmed computing at the Universities of Cambridge
and Illinois in the early fifties / David J. Wheeler /
269--279 \\
Early numerical analysis in the United Kingdom / L. Fox
/ 280--300 \\
The pioneer days of scientific computing in Switzerland
/ Martin H. Gutknecht / 301--313 \\
The development of computational mathematics in
Czechoslovakia and the USSR / I. Babuska / 314--328 \\
The contribution of Leningrad mathematicians to the
development of numerical linear algebra, 1950--1986 /
V. N. Kublanovskaya / 329--338",
}
@Book{Berggren:2000:PSB,
editor = "Lennart Berggren and Jonathan Borwein and Peter
Borwein",
booktitle = "Pi: a Source Book",
title = "Pi: a Source Book",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
pages = "xx + 736",
year = "2000",
DOI = "https://doi.org/10.1007/978-1-4757-3240-5",
ISBN = "0-387-98946-3 (hardcover)",
ISBN-13 = "978-0-387-98946-4 (hardcover)",
LCCN = "QA484 .P5 2000",
MRclass = "11-00 (01A05 01A75 11-03)",
MRnumber = "1746004",
bibdate = "Wed Aug 10 11:09:47 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
https://www.math.utah.edu/pub/tex/bib/agm.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib",
acknowledgement = ack-nhfb,
author-dates = "John Todd (16 May 1911--21 June 2007); Jonathan
Michael Borwein (20 May 1951--2 August 2016)",
libnote = "Not yet in my library.",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
subject = "Pi (mathematical constant)",
tableofcontents = "Preface / v \\
\\
Preface to the Second Edition / viii \\
Acknowledgments / ix \\
\\
Introduction / xvii \\
\\
1. The Rhind Mathematical Papyrus-Problem 50 ($\approx$
1650 B.C.) / A problem dealing with the area of a round
field of given diameter / 1 \\
\\
2. Engels. Quadrature of the Circle in Ancient Egypt
(1977) / A conjectural explanation of how the
mathematicians of ancient Egypt approximated the area
of a circle / 3 \\
\\
3. Archimedes. Measurement of a Circle ($\approx$ 250
BC) / The seminal work in which Archimedes presents the
first true algorithm for $\pi$ / 7 \\
\\
4. Phillips. Archimedes the Numerical Analyst (1981) /
A summary of Archimedes' work on the computation of
$\pi$ using modern notation / 15 \\
\\
5. Lam and Ang. Circle Measurements in Ancient China
(1986) / This paper discusses and contains a
translation of Liu Hui's (3rd century) method for
evaluating $\pi$ and also examines values for $\pi$
given by Zu Chongzhi (429--500) / 20 \\
\\
6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane
and Solid Figures ($\approx$ 850) / This extract gives
an explicit statement and proof that the ratio of the
circumference to the diameter is constant / 36 \\
\\
7. M{\=a}dhava. The Power Series for Arctan and Pi
($\approx$ 1400) / These theorems by a fifteenth
century Indian mathematician give Gregory's series for
arctan with remainder terms and Leibniz's series for
$\pi$ / 45 \\
\\
8. Hope-Jones. Ludolph (or Ludolff or Lucius) van
Ceulen (1938) / Correspondence about van Ceulen's
tombstone in reference to it containing some digits of
$\pi$ / 51 \\
\\
9. Vi{\'e}te. Variorum de Rebus Mathematicis Reponsorum
Liber VII (1593) / Two excerpts. One containing the
first infinite expression of $\pi$, obtained by
relating the area of a regular $2n$-gon to that of a
regular $n$-gon / 53 \\
\\
10. Wallis. Computation of $\pi$ by Successive
Interpolations (1655) / How Wallis derived the infinite
product for $\pi$ that bears his name / 68 \\
\\
11. Wallis. Arithmetica Infinitorum (1655) / An excerpt
including Prop. 189, 191 and an alternate form of the
result that gives Wm. Brounker's continued fraction
expression for $4/\pi$ / 78 \\
\\
12. Huygens. De Circuli Magnitudine Inventa (1724) /
Huygens's proof of W. Snell's discovery of improvements
in Archimedes' method of estimating the lengths of
circular arcs / 81 \\
\\
13. Gregory. Correspondence with John Collins (1671) /
A letter to Collins in which he gives his series for
arctangent, carried to the ninth power. / 87 \\
\\
14. Roy. The Discovery of the Series Formula for $\pi$
by Leibniz, Gregory, and Nilakantha (1990) / A
discussion of the discovery of the series $\pi/4 = 1 -
1/3 + 1/5, \cdots{}$ / 92 \\
\\
15. Jones. The First Use of $\pi$ for the Circle Ratio
(1706) / An excerpt from Jones' book, the Synopsis
Palmariorum Matheseos: or, a New Introduction to the
Mathematics, London, 1706 / 108 \\
\\
16. Newton. Of the Method of Fluxions and Infinite
Series (1737) / An excerpt giving Newton's calculation
of $\pi$ to 16 decimal places / 110 \\
\\
17. Euler. Chapter 10 of Introduction to Analysis of
the Infinite (On the Use of the Discovered Fractions to
Sum Infinite Series) (1748) / This includes many of
Euler's infinite series for $\pi$ and powers of $\pi$ /
112 \\
\\
18. Lambert. M{\'e}moire Sur Quelques
Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s
Transcendentes Circulaires et Logarithmiques (1761) /
An excerpt from Lambert's original proof of the
irrationality of $\pi$ / 129 \\
\\
19. Lambert. Irrationality of $\pi$ (1969) / A
translation and Struik's discussion of Lambert's proof
of the irrationality of $\pi$ / 141 \\
\\
20. Shanks. Contributions to Mathematics Comprising
Chiefly of the Rectification of the Circle to 607
Places of Decimals (1853) / Pages from Shank's report
of his monumental hand calculation of $\pi$ / 147 \\
\\
21. Hermite. Sur La Fonction Exponentielle (1873) / The
first proof of the transcendence of $e$ / 162 \\
\\
22. Lindemann. Ueber die Zahl $\pi$ (1882) / The first
proof of the transcendence of $\pi$ / 194 \\
\\
23. Weierstrass. Zu Lindemann's Abhandlung ``Uber die
Ludolphsche Zahl'' (1885) / Weierstrass' proof of the
transcendence of $\pi$ / 207 \\
\\
24. Hilbert. Ueber die Trancendenz der Zahlen $e$ und
$\pi$ (1893) / Hilbert's short and elegant
simplification of the transcendence proofs for $e$ and
$\pi$ / 226 \\
\\
25. Goodwin. Quadrature of the Circle (1894) / The
dubious origin of the attempted legislation of the
value of $\pi$ in Indiana / 230 \\
\\
26. Edington. House Bill No. 246, Indiana State
Legislature, 1897 (1935) / A summary of the action
taken by the Indiana State Legislature to fix the value
of $\pi$ (including a copy of the actual bill that was
proposed) / 231 \\
\\
27. Singmaster. The Legal Values of Pi (1985) / A
history of the attempt by Indiana to legislate the
value of $\pi$ / 236 \\
\\
28. Ramanujan. Squaring the Circle (1913) / A geometric
approximation to $\pi$ / 240 \\
\\
29. Ramanujan. Modular Equations and Approximations to
$\pi$ (1914) / Ramanujan's seminal paper on $\pi$ that
includes a number of striking series and algebraic
approximations / 241 \\
\\
30. Watson. The Marquis and the Land Agent: A Tale of
the Eighteenth Century (1933) / A Presidential address
to the Mathematical Association in which the author
gives an account of ``some of the elementary work on
arcs and ellipses and other curves which led up to the
idea of inverting an elliptic integral, and so laying
the foundations of elliptic functions and doubly
periodic functions generally.'' / 258 \\
\\
31. Ballantine. The Best (?) Formula for Computing
$\pi$ to a Thousand Places (1939) / An early attempt to
orchestrate the calculation of $\pi$ more cleverly /
271 \\
\\
32. Birch. An Algorithm for Construction of Arctangent
Relations (1946) / The object of this note is to
express $\pi / 4 $ as a sum of arctan relations in
powers of 10 / 274 \\
\\
33. Niven. A Simple Proof that $\pi$ Is Irrational
(1947) / A very concise proof of the irrationality of
$\pi$ / 276 \\
\\
34. Reitwiesner. An ENIAC Determination of $\pi$ and
$e$ to 2000 Decimal Places (1950) / One of the first
computer-based computations / 277 \\
\\
35. Schepler. The Chronology of Pi (1950) / A fairly
reliable outline of the history of $\pi$ from 3000 BC
to 1949 / 282 \\
\\
36. Mahler. On the Approximation of $\pi$ (1953) /
``The aim of this paper is to determine an explicit
lower bound free of unknown constants for the distance
of $\pi$ from a given rational or algebraic number'' /
306 \\
\\
37. Wrench, Jr. The Evolution of Extended Decimal
Approximations to $\pi$ (1960) / A history of the
calculation of the digits of $\pi$ to 1960 \\
\\
38. Shanks and Wrench, Jr. Calculation of $\pi$ to
100,000 Decimals (1962) / A landmark computation of
$\pi$ to more than 100,000 places / 326 \\
\\
39. Sweeny. On the Computation of Euler's Constant
(1963) / The computation of Euler's constant to 3566
decimal places / 350 \\
\\
40. Baker. Approximations to the Logarithms of Certain
Rational Numbers (1964) / The main purpose of this deep
and fundamental paper is to ``deduce results concerning
the accuracy with which the natural logarithms of
certain rational numbers may be approximated by
rational numbers, or, more generally, by algebraic
numbers of bounded degree.'' / 359 \\
\\
41. Adams. Asymptotic Diophantine Approximations to $E$
(1966) / An asymptotic estimate for the rational
approximation to $e$ which disproves the conjecture
that $e$ behaves like almost all numbers in this
respect / 368 \\
\\
42. Mahler. Applications of Some Formulae by Hermite to
the Approximations of Exponentials of Logarithms (1967)
/ An important extension of Hilbert's approach to the
study of transcendence / 372 \\
\\
43. Eves. In Mathematical Circles; A Selection of
Mathematical Stories and Anecdotes (excerpt) (1969) / A
collection of mathematical stories and anecdotes about
$\pi$ / 400 \\
\\
44. Eves. Mathematical Circles Revisited; A Second
Collection of Mathematical Stories and Anecdotes
(excerpt) (1971) / A further collection of mathematical
stories and anecdotes about $\pi$ / 402 \\
\\
45. Todd. The Lemniscate Constants (1975) / A unifying
account of some of the methods used for computing the
lemniscate constants / 412 \\
\\
46. Salamin. Computation of r Using
Arithmetic-Geometric Mean (1976) / The first
quadratically converging algorithm for $\pi$ based on
Gauss's AGM and on Legendre's relation for elliptic
integrals / 418 \\
\\
47. Brent. Fast Multiple-Precision Evaluation of
Elementary Functions (1976) / ``This paper contains the
`Gauss-Legendre' method and some different algorithms
for log and exp (using Landen transformations).'' / 424
\\
\\
48. Beukers. A Note on the Irrationality of $\zeta(2)$
and $\zetq(3)$ (1979) / A short and elegant recasting
of Ap{\'e}ry's proof of the irrationality of $\zeta(3)$
(and $\zeta(2)$) / 434 \\
\\
49. van der Poorten. A Proof that Euler Missed \ldots{}
Ap{\'e}ry's Proof of the Irrationality of $\zeta(3)$
(1979) / An illuminating account of Ap{\'e}ry's
astonishing proof of the irrationality of $\zeta(3)$ /
439 \\
\\
50. Brent and McMillan. Some New Algorithms for
High-Precision Computation of Euler's Constant (1980) /
Several new algorithms for high precision calculation
of Euler's constant, including one which was used to
compute 30,100 decimal places / 448 \\
\\
51. Apostol. A Proof that Euler Missed: Evaluating
$\zeta(2)$ the Easy Way (1983) / This note shows that
one of the double integrals considered by Beukers ([48]
in the table of contents) can be used to establish
directly that $\zeta(2) = \pi / 6$ / 456 \\
\\
52. O'Shaughnessy. Putting God Back in Math (1983) / An
article about the Institute of Pi Research, an
organization that ``pokes fun at creationists by
pointing out that even the Bible makes mistakes.'' /
458 \\
\\
53. Stern. A Remarkable Approximation to $\pi$ (1985) /
Justification of the value of $\pi$ in the Bible
through numerological interpretations / 460 \\
\\
54. Newman and Shanks. On a Sequence Arising in Series
for $\pi$ (1984) / More connections between $\pi$ and
modular equations / 462 \\
\\
55. Cox. The Arithmetic-Geometric Mean of Gauss (1984)
/ An extensive study of the complex analytic properties
of the AGM / 481 \\
\\
56. Borwein and Borwein. The Arithmetic-Geometric Mean
and Fast Computation of Elementary Functions (1984) /
The relationship between the AGM iteration and fast
computation of elementary functions (one of the
by-products is an algorithm for $\pi$) / 537 \\
\\
57. Newman. A Simplified Version of the Fast Algorithms
of Brent and Salamin (1984) / Elementary algorithms for
evaluating $e^x$ and $\pi$ using the Gauss AGM without
explicit elliptic function theory / 553 \\
\\
58. Wagon. Is Pi Normal? (1985) / A discussion of the
conjecture that $\pi$ has randomly distributed digits /
557 \\
\\
59. Keith. Circle Digits: A Self-Referential Story
(1986) / A mnemonic for the first 402 decimal places of
$\pi$ / 560 \\
\\
60. Bailey. The Computation of $\pi$ to 29,360,000
Decimal Digits Using Borweins' Quartically Convergent
Algorithm (1988) / The algorithms used, both for $\pi$
and for performing the required multiple-precision
arithmetic / 562 \\
\\
61. Kanada. Vectorization of Multiple-Precision
Arithmetic Program and 201,326,000 Decimal Digits of 1
Calculation (1988) / Details of the computation and
statistical tests of the first 200 million digits of
$\pi$ / 576 \\
\\
62. Borwein and Borwein. Ramanujan and Pi (1988) / This
article documents Ramanujan's life, his ingenious
approach to calculating $\pi$, and how his approach is
now incorporated into modern computer algorithms / 588
\\
\\
63. Chudnovsky and Chudnovsky. Approximations and
Complex Multiplication According to Ramanujan (1988) /
This excerpt describes ``Ramanujan's original quadratic
period--quasiperiod relations for elliptic curves with
complex multiplication and their applications to
representations of fractions of $\pi$ and other
logarithms in terms of rapidly convergent nearly
integral (hypergeometric) series.'' / 596 \\
\\
64. Borwein, Borwein and Bailey. Ramanujan, Modular
Equations, and Approximations to Pi or How to Compute
One Billion Digits of Pi (1989) / An exposition of the
computation of $\pi$ using mathematics rooted in
Ramanujan's work / 623 \\
\\
65. Borwein, Borwein and Dilcher. Pi, Euler Numbers,
and Asymptotic Expansions (1989) / An explanation as to
why the slowly convergent Gregory series for $\pi$,
truncated at 500,000 terms, gives $\pi$ to 40 places
with only the 6th, 17th, 18th, and 29th places being
incorrect / 642 \\
\\
66. Beukers, B{\'e}zivin, and Robba. An Alternative
Proof of the Lindemann--Weierstrass Theorem (1990) /
The Lindemann--Weierstrass theorem as a by-product of a
criterion for rationality of solutions of differential
equations / 649 \\
\\
67. Webster. The Tail of Pi (1991) / Various anecdotes
about $\pi$ from the 14th annual IMO Lecture to the
Royal Society / 654 \\
\\
68. Eco. An excerpt from Foucault's Pendulum (1993) /
``The unnumbered perfection of the circle itself.'' /
658 \\
\\
69. Keith. Pi Mnemonics and the Art of Constrained
Writing (1996) / A mnemonic for $\pi$ based on Edgar
Allen Poe's poem ``The Raven.'' / 659 \\
\\
70. Bailey, Borwein, and Plouffe. On the Rapid
Computation of Various Polylogarithmic Constants (1996)
/ A fast method for computing individual digits of
$\pi$ in base 2 / 663 \\
Appendix I --- On the Early History of Pi / 677 \\
\\
Appendix II --- A Computational Chronology of Pi / 683
\\
\\
Appendix III --- Selected Formulae for Pi / 686 \\
\\
Appendix IV --- Translations of Vi{\`e}te and Huygens /
690 \\
Bibliography / 711 \\
\\
Credits / 717 \\
\\
Index / 721",
}
