%%====================================================================== %% WARNING: Do NOT edit this file. It was produced automatically %% with the UNIX pipeline %% %% biblex xxx.bib | \ %% gawk -f keywords.awk | \ %% egrep 'entrytype$' | \ %% gawk -f fmtwords.awk >xxx.xwx %% %% by beebe@gamma.math.utah.edu on Thu Aug 29 10:23:51 MDT 2024 %%====================================================================== \ifx \NAMECITE \undefined % User can override this definition \def \NAMECITE #1#2{{\bf #1} \cite{#2}} \fi \NAMECITE{$p$}{% Chi:2021:MPB% }. \NAMECITE{$ Q R $}{% Chandrasekaran:1991:RRF,% Chandrasekaran:1994:RRF,% Chandrasekaran:1995:AAC,% Holodnak:2015:CLS,% Ipsen:1984:PMU% }. \NAMECITE{$ \sin \Theta $}{% Ipsen:2000:ORT% }. \NAMECITE{-norms}{% Chi:2021:MPB% }. \NAMECITE{{14th}}{% Ipsen:2009:PIC,% Ipsen:2009:SID% }. \NAMECITE{{2004}}{% Ipsen:2006:SIP% }. \NAMECITE{{2007}}{% Ipsen:2009:PIC,% Ipsen:2009:SID% }. \NAMECITE{'92}{% Jiang:1994:NAP% }. \NAMECITE{Absolute}{% Eisenstat:1998:TAP,% Ipsen:2000:ARP,% Eisenstat:1999:TAP,% Ipsen:2003:NUA% }. \NAMECITE{Accuracy}{% Banoczi:1998:LIR,% Jessup:1992:IAI% }. \NAMECITE{accurate}{% Ipsen:2006:SIA,% Ipsen:2006:SIP,% Ipsen:2009:SIA% }. \NAMECITE{Active}{% Holodnak:2018:PSB% }. \NAMECITE{Advanced}{% Golub:1988:NAS% }. \NAMECITE{Algebra}{% Golub:1988:NAS,% Ipsen:2009:SID,% Jiang:1994:NAP,% Lewis:1994:ALA% }. \NAMECITE{Algorithm}{% Chandrasekaran:1994:DCA,% Chandrasekaran:1995:AQA,% Delosme:1989:BAS,% Eriksson-Bique:2011:ISM,% Ipsen:2005:CAP,% Chandrasekaran:1995:AAC,% Ipsen:2006:CAP% }. \NAMECITE{Algorithms}{% Delosme:1990:PCA,% Golub:1988:NAS,% Ipsen:1987:SAP,% Ipsen:1988:SAP,% Ipsen:1990:SRG,% Schultz:1988:NAM,% Ipsen:1991:SRG% }. \NAMECITE{Analysis}{% Chandrasekaran:1995:AAC,% Chandrasekaran:1995:AQA,% Ipsen:2005:CAP,% Ipsen:2020:PEA,% Ipsen:2006:CAP,% Ipsen:2006:MPA,% Ipsen:2009:NMA% }. \NAMECITE{Angeles}{% Rodrigue:1989:PPS% }. \NAMECITE{Angle}{% Ipsen:1995:ABC% }. \NAMECITE{Application}{% Eriksson-Bique:2011:ISM,% Heller:1982:SNO,% Holodnak:2018:PSB% }. \NAMECITE{Applications}{% Jiang:1994:NAP% }. \NAMECITE{Applied}{% Lewis:1994:ALA,% Finkel:2006:CAM% }. \NAMECITE{approach}{% Chi:2022:PBA% }. \NAMECITE{Approximation}{% Drineas:2018:SCR,% Holodnak:2015:RAG% }. \NAMECITE{Approximations}{% Drineas:2019:LRM% }. \NAMECITE{Architectures}{% Delosme:1987:ESA,% Ipsen:1985:IPA,% Ipsen:1986:IPA,% Schultz:1988:NAM% }. \NAMECITE{arclength}{% Dickson:2007:CEP% }. \NAMECITE{array}{% Delosme:1986:SAS% }. \NAMECITE{Arrays}{% Barlow:1987:SGR,% Delosme:1987:ESA,% Ipsen:1984:SVD% }. \NAMECITE{Attention}{% Ipsen:2008:PCS,% Ipsen:2007:PCS% }. \NAMECITE{Austria}{% Cullum:1986:LSE% }. \NAMECITE{aware}{% Hallman:2023:PAD% }. \NAMECITE{Backward}{% Chandrasekaran:1994:BEE% }. \NAMECITE{{Bareiss}}{% Delosme:1989:BAS,% Ipsen:1990:SRG,% Ipsen:1991:SRG% }. \NAMECITE{based}{% Chi:2022:PBA% }. \NAMECITE{{BayesCG}}{% Reid:2023:SPB% }. \NAMECITE{{Bayesian}}{% Cockayne:2019:BCG% }. \NAMECITE{behind}{% Ipsen:1998:IBK% }. \NAMECITE{Belgium}{% Golub:1988:NAS% }. \NAMECITE{Between}{% Ipsen:1995:ABC% }. \NAMECITE{Block}{% Drineas:2018:SCR% }. \NAMECITE{Bound}{% Holodnak:2018:PSB% }. \NAMECITE{Bounds}{% Eisenstat:1994:RPB,% Eisenstat:1998:TAP,% Holodnak:2015:RAG,% Chi:2021:MPB,% Eisenstat:1999:TAP,% Hallman:2023:PAD,% Ipsen:2000:ARP,% Ipsen:2000:EBG,% Ipsen:2003:NUA,% Ipsen:2008:PBD,% Ipsen:2009:RPB% }. \NAMECITE{California}{% Rodrigue:1989:PPS% }. \NAMECITE{Can}{% Boutsikas:2024:SSV% }. \NAMECITE{{Carlo}}{% Eriksson-Bique:2011:ISM,% Hallman:2023:MCM% }. \NAMECITE{Chains}{% Ipsen:1994:USM% }. \NAMECITE{Characteristic}{% Rehman:2011:CCP,% Ipsen:2008:PBD% }. \NAMECITE{Chicago}{% Dongarra:1990:PPS% }. \NAMECITE{China}{% Ipsen:2009:SID% }. \NAMECITE{Code}{% Gropp:1989:GCS% }. \NAMECITE{Coefficients}{% Ipsen:2011:ECD% }. \NAMECITE{Coherence}{% Ipsen:2014:ECS% }. \NAMECITE{Columns}{% Ipsen:2014:ECS% }. \NAMECITE{Communicating}{% Finkel:2006:CAM% }. \NAMECITE{Complementary}{% Ipsen:1995:ABC% }. \NAMECITE{Complex}{% Ipsen:1996:HWC,% Ipsen:2000:ORT% }. \NAMECITE{Complexity}{% Ipsen:1984:CDL,% Ipsen:1986:CDL% }. \NAMECITE{Components}{% Chandrasekaran:1995:SSC% }. \NAMECITE{computability}{% Delosme:1986:SAS% }. \NAMECITE{Computation}{% Delosme:1989:BAS,% Delosme:1990:PCA,% Holodnak:2015:CLS,% Holodnak:2015:RAG,% Ipsen:2008:PCS,% Ipsen:2007:PCS% }. \NAMECITE{Computations}{% Ipsen:1983:SMC% }. \NAMECITE{Computer}{% Schultz:1988:NAM% }. \NAMECITE{Computing}{% Chandrasekaran:1994:DCA,% Chandrasekaran:1995:AQA,% Delosme:1987:CPC,% Dongarra:1990:PPS,% Ipsen:1997:CEI,% Rehman:2011:CCP,% Chandrasekaran:1995:AAC,% Rodrigue:1989:PPS% }. \NAMECITE{Condition}{% Dickson:2007:CEP% }. \NAMECITE{Conditioning}{% Holodnak:2015:CLS% }. \NAMECITE{cones}{% Delosme:1986:SAS% }. \NAMECITE{Conference}{% Dongarra:1990:PPS,% Ipsen:2009:PIC,% Jiang:1994:NAP,% Lewis:1994:ALA,% Rodrigue:1989:PPS,% Ipsen:2009:SID% }. \NAMECITE{Conjugate}{% Cockayne:2019:BCG% }. \NAMECITE{Conquer}{% Chandrasekaran:1994:DCA% }. \NAMECITE{Construction}{% Delosme:1987:ESA% }. \NAMECITE{continuation}{% Dickson:2007:CEP% }. \NAMECITE{Contributions}{% Ipsen:1996:HWC% }. \NAMECITE{Convergence}{% Campbell:1995:CES,% Campbell:1996:CES,% Drineas:2018:SCR,% Ipsen:2005:CAP,% Ipsen:2006:CAP% }. \NAMECITE{Correlations}{% Delosme:1987:CPC,% Delosme:1989:BAS% }. \NAMECITE{Dangling}{% Ipsen:2008:PCS,% Ipsen:2007:PCS% }. \NAMECITE{Data}{% Delosme:1987:CPC% }. \NAMECITE{December}{% Dongarra:1990:PPS,% Rodrigue:1989:PPS% }. \NAMECITE{Decomposition}{% Chandrasekaran:1994:SVD,% Holodnak:2015:CLS,% Ipsen:1984:SVD% }. \NAMECITE{Decompositions}{% Chandrasekaran:1994:BEE,% Heller:1983:SNO% }. \NAMECITE{Deficient}{% Ipsen:2011:RDN% }. \NAMECITE{Defined}{% Ipsen:2011:ECD% }. \NAMECITE{Definite}{% Delosme:1986:PSS,% Ipsen:1987:SAP,% Ipsen:1988:SAP% }. \NAMECITE{Dense}{% Ipsen:1984:CDL,% Ipsen:1986:CDL,% Ipsen:1987:SAP,% Ipsen:1988:SAP% }. \NAMECITE{Dense-Linear-System}{% Ipsen:1986:CDL% }. \NAMECITE{Dependences}{% Delosme:1990:PCA% }. \NAMECITE{determinant}{% Saibaba:2017:RMF% }. \NAMECITE{determinants}{% Ipsen:2008:PBD% }. \NAMECITE{deterministic}{% Hallman:2023:PAD% }. \NAMECITE{devoted}{% Ipsen:2009:SID% }. \NAMECITE{Diagonal}{% Hallman:2023:MCM% }. \NAMECITE{diagonalisable}{% Eisenstat:1998:RPR% }. \NAMECITE{Digital}{% Golub:1988:NAS% }. \NAMECITE{Discussion}{% Cockayne:2019:BCG% }. \NAMECITE{Divide}{% Chandrasekaran:1994:DCA% }. \NAMECITE{Do}{% Drineas:2019:LRM% }. \NAMECITE{Dominant}{% Drineas:2018:SCR% }. \NAMECITE{edition}{% Girolami:2019:ESE% }. \NAMECITE{Editorial}{% Girolami:2019:ESE% }. \NAMECITE{Effect}{% Ipsen:2014:ECS% }. \NAMECITE{Efficient}{% Delosme:1987:ESA% }. \NAMECITE{eigenproblem}{% Ipsen:2010:EIS% }. \NAMECITE{Eigenspaces}{% Eisenstat:1994:RPB% }. \NAMECITE{Eigenvalue}{% Chandrasekaran:1994:BEE,% Ipsen:1985:IPA,% Ipsen:1986:IPA,% Ipsen:1987:SST,% Ipsen:1990:SST,% Ipsen:1996:HWC,% Cullum:1986:LSE,% Ipsen:1987:TMS,% Ipsen:2006:SIA,% Ipsen:2006:SIP,% Ipsen:2009:SIA% }. \NAMECITE{Eigenvalues}{% Eisenstat:1998:TAP,% Rehman:2011:CCP,% Beattie:2003:IRM,% Eisenstat:1998:RPR,% Eisenstat:1999:TAP,% Ipsen:1998:RPR,% Ipsen:2009:RPB% }. \NAMECITE{Eigenvector}{% Ipsen:1997:CEI% }. \NAMECITE{eigenvectors}{% Eisenstat:1998:RPR% }. \NAMECITE{Embed}{% Bhatt:1985:HET% }. \NAMECITE{Equations}{% Campbell:1995:CES,% Chandrasekaran:1995:SSC,% Campbell:1996:CES% }. \NAMECITE{Equivalence}{% Heller:1982:SNO% }. \NAMECITE{Ergodicity}{% Ipsen:2011:ECD% }. \NAMECITE{Error}{% Ipsen:2020:PEA,% Hallman:2023:PAD% }. \NAMECITE{Errors}{% Chandrasekaran:1994:BEE% }. \NAMECITE{Estimates}{% Campbell:1995:CES,% Campbell:1996:CES,% Dickson:2007:CEP% }. \NAMECITE{Estimating}{% Hallman:2023:MCM% }. \NAMECITE{estimators}{% Saibaba:2017:RMF% }. \NAMECITE{Europe}{% Cullum:1986:LSE% }. \NAMECITE{Exact}{% Holodnak:2015:RAG% }. \NAMECITE{examples}{% Finkel:2006:CAM% }. \NAMECITE{excess}{% Chi:2022:PBA% }. \NAMECITE{Expository}{% Ipsen:2010:ERPa,% Ipsen:2010:ERPb,% Ipsen:2010:ERPc,% Ipsen:2010:ERPd,% Ipsen:2011:ERPa,% Ipsen:2011:ERPb,% Ipsen:2011:ERPc,% Ipsen:2011:ERPd,% Ipsen:2012:ERP% }. \NAMECITE{Expressions}{% Ipsen:2000:EBG% }. \NAMECITE{Factorisations}{% Chandrasekaran:1991:RRF,% Chandrasekaran:1994:RRF% }. \NAMECITE{Fast}{% Ipsen:1984:PMU% }. \NAMECITE{Fifth}{% Lewis:1994:ALA% }. \NAMECITE{floating}{% Hallman:2023:PAD% }. \NAMECITE{four}{% Finkel:2006:CAM% }. \NAMECITE{Fourth}{% Dongarra:1990:PPS% }. \NAMECITE{free}{% Saibaba:2017:RMF% }. \NAMECITE{Functions}{% Beckermann:2018:LRU% }. \NAMECITE{Gap}{% Drineas:2019:LRM% }. \NAMECITE{Generalised}{% Ipsen:1990:SRG,% Ipsen:1991:SRG% }. \NAMECITE{Germany}{% Ipsen:2006:SIP% }. \NAMECITE{{Givens'}}{% Ipsen:1984:PMU,% Barlow:1987:SGR% }. \NAMECITE{{GMRES}}{% Campbell:1994:GMP,% Campbell:1995:CES,% Campbell:1996:CES,% Campbell:1996:GMP,% Ipsen:2000:EBG% }. \NAMECITE{{Google}}{% Ipsen:2006:MPA,% Wills:2008:ORG,% Wills:2009:ORG% }. \NAMECITE{Gradient}{% Cockayne:2019:BCG% }. \NAMECITE{{Gram}}{% Holodnak:2015:RAG% }. \NAMECITE{{Gray}}{% Gropp:1989:GCS% }. \NAMECITE{{Hagen}}{% Ipsen:2006:SIP% }. \NAMECITE{Hand}{% Banoczi:1998:LIR% }. \NAMECITE{held}{% Cullum:1986:LSE,% Rodrigue:1989:PPS% }. \NAMECITE{{Helmut}}{% Ipsen:1996:HWC% }. \NAMECITE{{Hermitian}}{% Ipsen:2009:RPB% }. \NAMECITE{History}{% Ipsen:1994:HII,% Ipsen:1996:HII% }. \NAMECITE{Hyperbolic}{% Delosme:1986:PSS% }. \NAMECITE{Hypercube}{% Ipsen:1987:SST,% Ipsen:1990:SST,% Ipsen:1987:TMS% }. \NAMECITE{Hypercubes}{% Bhatt:1985:HET,% Gropp:1988:RMR,% Gropp:1989:GCS,% Gropp:1989:RMR% }. \NAMECITE{{IBM}}{% Cullum:1986:LSE% }. \NAMECITE{idea}{% Ipsen:1998:IBK% }. \NAMECITE{ILAS}{% Ipsen:2009:PIC,% Ipsen:2009:SID% }. \NAMECITE{Illinois}{% Dongarra:1990:PPS% }. \NAMECITE{Illustration}{% Delosme:1987:ESA% }. \NAMECITE{Impact}{% Ipsen:1985:IPA,% Ipsen:1986:IPA% }. \NAMECITE{Imply}{% Eisenstat:1998:TAP,% Eisenstat:1999:TAP% }. \NAMECITE{Importance}{% Eriksson-Bique:2011:ISM% }. \NAMECITE{Improving}{% Jessup:1992:IAI% }. \NAMECITE{Inclusion}{% Beattie:2003:IRM% }. \NAMECITE{Increase}{% Boutsikas:2024:SSV% }. \NAMECITE{Influence}{% Banoczi:1998:LIR% }. \NAMECITE{Information}{% Eriksson-Bique:2011:ISM% }. \NAMECITE{Inner}{% Ipsen:2020:PEA% }. \NAMECITE{Institute}{% Cullum:1986:LSE,% Golub:1988:NAS% }. \NAMECITE{Integral}{% Campbell:1995:CES,% Campbell:1996:CES% }. \NAMECITE{International}{% Ipsen:2009:SID,% Jiang:1994:NAP,% Ipsen:2006:SIP% }. \NAMECITE{Introduction}{% Ipsen:2007:I,% Ipsen:2008:I,% Ipsen:2008:PTIa,% Ipsen:2008:PTIb,% Ipsen:2009:PTI% }. \NAMECITE{invariant}{% Ipsen:2000:ARP,% Ipsen:2000:ORT,% Ipsen:2010:EIS% }. \NAMECITE{Inverse}{% Ipsen:1994:HII,% Ipsen:1996:HII,% Ipsen:1997:CEI,% Jessup:1992:IAI% }. \NAMECITE{issue}{% Ipsen:2006:SIA,% Ipsen:2006:SIP,% Ipsen:2009:SIA,% Ipsen:2009:SID% }. \NAMECITE{Iteration}{% Ipsen:1994:HII,% Ipsen:1996:HII,% Ipsen:1997:CEI,% Jessup:1992:IAI% }. \NAMECITE{Iterative}{% Cockayne:2021:PIM% }. \NAMECITE{July}{% Cullum:1986:LSE,% Ipsen:2006:SIP,% Ipsen:2009:SID% }. \NAMECITE{June}{% Ipsen:2006:SIP,% Lewis:1994:ALA% }. \NAMECITE{{Krylov}}{% Drineas:2018:SCR,% Ipsen:1998:IBK,% Reid:2023:SPB% }. \NAMECITE{Lack}{% Banoczi:1998:LIR% }. \NAMECITE{{Langville}}{% Ipsen:2005:CAP,% Ipsen:2006:CAP% }. \NAMECITE{Large}{% Cullum:1986:LSE% }. \NAMECITE{Least}{% Barlow:1987:SGR,% Ipsen:2011:RDN,% Ipsen:2014:ECS% }. \NAMECITE{Leuven}{% Golub:1988:NAS% }. \NAMECITE{Leverage}{% Holodnak:2015:CLS% }. \NAMECITE{{Levinson}}{% Ipsen:1990:SRG,% Ipsen:1991:SRG% }. \NAMECITE{Linear}{% Banoczi:1998:LIR,% Barlow:1987:SGR,% Chandrasekaran:1995:SSC,% Cockayne:2021:PIM,% Golub:1988:NAS,% Ipsen:1984:CDL,% Ipsen:1986:CDL,% Ipsen:2009:SID,% Lewis:1994:ALA,% Bartels:2019:PLS,% Chi:2021:MPB,% Chi:2022:PBA% }. \NAMECITE{Local}{% Gropp:1989:GCS% }. \NAMECITE{log}{% Saibaba:2017:RMF% }. \NAMECITE{log-determinant}{% Saibaba:2017:RMF% }. \NAMECITE{Low}{% Beckermann:2018:LRU,% Drineas:2019:LRM% }. \NAMECITE{Low-Rank}{% Beckermann:2018:LRU,% Drineas:2019:LRM% }. \NAMECITE{Lower}{% Boutsikas:2024:SSV% }. \NAMECITE{{Markov}}{% Ipsen:1994:USM% }. \NAMECITE{Mathematical}{% Ipsen:2006:MPA% }. \NAMECITE{mathematics}{% Finkel:2006:CAM% }. \NAMECITE{Matrices}{% Chandrasekaran:1994:SVD,% Ipsen:2014:ECS,% Eisenstat:1998:RPR,% Ipsen:2000:ARP,% Ipsen:2000:ORT,% Ipsen:2001:NPN,% Ipsen:2009:RPB% }. \NAMECITE{Matrix}{% Beckermann:2018:LRU,% Delosme:1987:CPC,% Drineas:2019:LRM,% Eisenstat:1998:TAP,% Eriksson-Bique:2011:ISM,% Hallman:2023:MCM,% Holodnak:2015:RAG,% Ipsen:1983:SMC,% Beattie:2003:IRM,% Eisenstat:1999:TAP,% Ipsen:1998:RPR,% Ipsen:2009:NMA,% Saibaba:2017:RMF% }. \NAMECITE{matrix-free}{% Saibaba:2017:RMF% }. \NAMECITE{Mesh}{% Gropp:1988:RMR,% Gropp:1989:GCS,% Gropp:1989:RMR% }. \NAMECITE{Method}{% Cockayne:2019:BCG,% Ipsen:1984:PMU% }. \NAMECITE{Methodology}{% Delosme:1987:ESA% }. \NAMECITE{Methods}{% Cockayne:2021:PIM,% Hallman:2023:MCM,% Ipsen:1987:TMS,% Ipsen:1998:IBK% }. \NAMECITE{{Meyer}}{% Ipsen:2005:CAP,% Ipsen:2006:CAP% }. \NAMECITE{Minimal}{% Campbell:1994:GMP,% Campbell:1996:GMP% }. \NAMECITE{Modern}{% Schultz:1988:NAM% }. \NAMECITE{{Monte}}{% Eriksson-Bique:2011:ISM,% Hallman:2023:MCM% }. \NAMECITE{multiple}{% Chi:2021:MPB% }. \NAMECITE{Multiplication}{% Eriksson-Bique:2011:ISM% }. \NAMECITE{Multiplicative}{% Chi:2021:MPB% }. \NAMECITE{Multiprocessor}{% Ipsen:1984:CDL,% Ipsen:1986:CDL% }. \NAMECITE{multivariate}{% Chi:2021:MPB% }. \NAMECITE{{NATO}}{% Golub:1988:NAS% }. \NAMECITE{Need}{% Drineas:2019:LRM% }. \NAMECITE{Network}{% Heller:1982:SNO% }. \NAMECITE{Networks}{% Heller:1983:SNO% }. \NAMECITE{Nodes}{% Ipsen:2008:PCS,% Ipsen:2007:PCS% }. \NAMECITE{non}{% Ipsen:2009:RPB% }. \NAMECITE{non-{Hermitian}}{% Ipsen:2009:RPB% }. \NAMECITE{Nonlinear}{% Ipsen:2011:RDN% }. \NAMECITE{nonsymmetric}{% Ipsen:2001:NPN% }. \NAMECITE{Norms}{% Ipsen:2011:ECD,% Chi:2021:MPB% }. \NAMECITE{note}{% Ipsen:2001:NPN,% Ipsen:2003:NUA% }. \NAMECITE{Numerical}{% Ipsen:1996:HWC,% Ipsen:2009:NMA,% Jiang:1994:NAP,% Schultz:1988:NAM% }. \NAMECITE{numerics}{% Girolami:2019:ESE% }. \NAMECITE{Oberlech}{% Cullum:1986:LSE% }. \NAMECITE{Ordinal}{% Wills:2008:ORG,% Wills:2009:ORG% }. \NAMECITE{Orthogonal}{% Heller:1982:SNO,% Heller:1983:SNO% }. \NAMECITE{Orthonormal}{% Ipsen:2014:ECS% }. \NAMECITE{overview}{% Ipsen:2000:ORT% }. \NAMECITE{{PageRank}}{% Ipsen:2005:CAP,% Ipsen:2006:CAP,% Ipsen:2006:MPA,% Ipsen:2007:PCS,% Ipsen:2008:PCS,% Wills:2008:ORG,% Wills:2009:ORG% }. \NAMECITE{Papers}{% Ipsen:2010:ERPa,% Ipsen:2010:ERPb,% Ipsen:2010:ERPc,% Ipsen:2010:ERPd,% Ipsen:2011:ERPa,% Ipsen:2011:ERPb,% Ipsen:2011:ERPc,% Ipsen:2011:ERPd,% Ipsen:2012:ERP% }. \NAMECITE{Parallel}{% Delosme:1986:PSS,% Delosme:1990:PCA,% Dongarra:1990:PPS,% Golub:1988:NAS,% Ipsen:1984:PMU,% Ipsen:1985:IPA,% Ipsen:1986:IPA,% Ipsen:1987:SAP,% Ipsen:1988:SAP,% Rodrigue:1989:PPS,% Schultz:1988:NAM% }. \NAMECITE{Partial}{% Delosme:1987:CPC,% Delosme:1989:BAS% }. \NAMECITE{Perturbation}{% Eisenstat:1993:RPT,% Eisenstat:1994:RPB,% Eisenstat:1995:RPT,% Eisenstat:1998:TAP,% Ipsen:2008:PBD,% Chi:2021:MPB,% Eisenstat:1998:RPR,% Eisenstat:1999:TAP,% Ipsen:1998:RPR,% Ipsen:2000:ARP,% Ipsen:2003:NUA,% Ipsen:2009:RPB,% Ipsen:2010:EIS% }. \NAMECITE{point}{% Hallman:2023:PAD% }. \NAMECITE{Polynomial}{% Campbell:1994:GMP,% Campbell:1996:GMP% }. \NAMECITE{Polynomials}{% Rehman:2011:CCP,% Ipsen:2008:PBD% }. \NAMECITE{Positive}{% Delosme:1986:PSS,% Ipsen:1987:SAP,% Ipsen:1988:SAP% }. \NAMECITE{Positive-Definite}{% Ipsen:1987:SAP,% Ipsen:1988:SAP% }. \NAMECITE{Precision}{% Boutsikas:2024:SSV,% Hallman:2023:PAD% }. \NAMECITE{Precision-aware}{% Hallman:2023:PAD% }. \NAMECITE{Preconditioned}{% Ipsen:2014:ECS% }. \NAMECITE{preconditioning}{% Ipsen:2001:NPN% }. \NAMECITE{Preface}{% Barlow:2015:P,% Ipsen:2009:PIC% }. \NAMECITE{prior}{% Reid:2023:SPB% }. \NAMECITE{Probabilistic}{% Bartels:2019:PLS,% Cockayne:2021:PIM,% Holodnak:2015:RAG,% Holodnak:2018:PSB,% Ipsen:2020:PEA,% Girolami:2019:ESE,% Hallman:2023:PAD% }. \NAMECITE{Problem}{% Ipsen:1987:SST,% Ipsen:1990:SST,% Ipsen:1987:TMS% }. \NAMECITE{Problems}{% Barlow:1987:SGR,% Eisenstat:1993:RPT,% Eisenstat:1995:RPT,% Ipsen:1985:IPA,% Ipsen:1986:IPA,% Ipsen:1996:HWC,% Ipsen:2005:PT,% Ipsen:2006:PTa,% Ipsen:2006:PTb,% Ipsen:2006:PTc,% Ipsen:2006:PTd,% Ipsen:2007:PT,% Ipsen:2007:PTa,% Ipsen:2007:PTb,% Ipsen:2007:PTc,% Ipsen:2007:PTd,% Ipsen:2008:PTIa,% Ipsen:2008:PTIb,% Ipsen:2008:PTa,% Ipsen:2008:PTd,% Ipsen:2009:PTI,% Ipsen:2009:PTa,% Ipsen:2009:PTb,% Ipsen:2009:PTc,% Ipsen:2011:RDN,% Ipsen:2014:ECS,% Cullum:1986:LSE,% Ipsen:2006:SIA,% Ipsen:2006:SIP,% Ipsen:2009:SIA% }. \NAMECITE{Proceedings}{% Dongarra:1990:PPS,% Ipsen:2006:SIP,% Ipsen:2009:PIC,% Jiang:1994:NAP,% Lewis:1994:ALA,% Rodrigue:1989:PPS,% Cullum:1986:LSE% }. \NAMECITE{Processing}{% Dongarra:1990:PPS,% Golub:1988:NAS,% Rodrigue:1989:PPS% }. \NAMECITE{Products}{% Ipsen:2020:PEA% }. \NAMECITE{projector}{% Chi:2022:PBA% }. \NAMECITE{projector-based}{% Chi:2022:PBA% }. \NAMECITE{properties}{% Ipsen:2006:MPA,% Reid:2023:SPB% }. \NAMECITE{pseudo}{% Dickson:2007:CEP% }. \NAMECITE{pseudo-arclength}{% Dickson:2007:CEP% }. \NAMECITE{{QR}}{% Chandrasekaran:1995:AQA% }. \NAMECITE{quantifying}{% Chi:2022:PBA% }. \NAMECITE{Randomized}{% Holodnak:2015:RAG,% Saibaba:2017:RMF% }. \NAMECITE{Rank}{% Beckermann:2018:LRU,% Chandrasekaran:1991:RRF,% Chandrasekaran:1994:RRF,% Drineas:2019:LRM,% Ipsen:2011:RDN% }. \NAMECITE{Rank-Deficient}{% Ipsen:2011:RDN% }. \NAMECITE{Rank-Revealing}{% Chandrasekaran:1991:RRF,% Chandrasekaran:1994:RRF% }. \NAMECITE{Ranking}{% Wills:2009:ORG,% Wills:2008:ORG% }. \NAMECITE{Real}{% Hallman:2023:MCM% }. \NAMECITE{Recursive}{% Gropp:1988:RMR,% Gropp:1989:RMR% }. \NAMECITE{Refined}{% Ipsen:2009:RPB% }. \NAMECITE{Refinement}{% Gropp:1988:RMR,% Gropp:1989:GCS,% Gropp:1989:RMR% }. \NAMECITE{regions}{% Beattie:2003:IRM% }. \NAMECITE{regression}{% Chi:2021:MPB,% Chi:2022:PBA% }. \NAMECITE{Relative}{% Eisenstat:1993:RPT,% Eisenstat:1994:RPB,% Eisenstat:1995:RPT,% Eisenstat:1998:RPR,% Eisenstat:1998:TAP,% Ipsen:1998:RPR,% Eisenstat:1999:TAP,% Ipsen:2000:ARP,% Ipsen:2000:ORT,% Ipsen:2003:NUA% }. \NAMECITE{Remarks}{% Ipsen:1990:SRG,% Ipsen:1991:SRG% }. \NAMECITE{Research}{% Ipsen:2010:ERPa,% Ipsen:2010:ERPb,% Ipsen:2010:ERPc,% Ipsen:2010:ERPd,% Ipsen:2011:ERPa,% Ipsen:2011:ERPb,% Ipsen:2011:ERPc,% Ipsen:2011:ERPd,% Ipsen:2012:ERP,% Ipsen:2012:RS% }. \NAMECITE{residual}{% Ipsen:2000:EBG% }. \NAMECITE{Results}{% Drineas:2018:SCR,% Eisenstat:1998:RPR,% Ipsen:1998:RPR% }. \NAMECITE{Retrieval}{% Eriksson-Bique:2011:ISM% }. \NAMECITE{Revealing}{% Chandrasekaran:1991:RRF,% Chandrasekaran:1994:RRF% }. \NAMECITE{Right}{% Banoczi:1998:LIR% }. \NAMECITE{Right-Hand}{% Banoczi:1998:LIR% }. \NAMECITE{Ring}{% Ipsen:1984:CDL,% Ipsen:1986:CDL% }. \NAMECITE{Rotations}{% Barlow:1987:SGR,% Delosme:1986:PSS,% Ipsen:1984:PMU% }. \NAMECITE{Sampling}{% Eriksson-Bique:2011:ISM,% Ipsen:2014:ECS% }. \NAMECITE{scale}{% Cullum:1986:LSE% }. \NAMECITE{Scaled}{% Barlow:1987:SGR% }. \NAMECITE{{Schatten}}{% Chi:2021:MPB% }. \NAMECITE{Scheme}{% Gropp:1989:GCS% }. \NAMECITE{Scientific}{% Dongarra:1990:PPS,% Rodrigue:1989:PPS% }. \NAMECITE{Scores}{% Holodnak:2015:CLS% }. \NAMECITE{Selection}{% Ipsen:2011:RDN% }. \NAMECITE{Sensitivity}{% Chandrasekaran:1995:SSC% }. \NAMECITE{Shanghai}{% Ipsen:2009:PIC,% Ipsen:2009:SID,% Jiang:1994:NAP% }. \NAMECITE{{SIAM}}{% Dongarra:1990:PPS,% Lewis:1994:ALA,% Rodrigue:1989:PPS% }. \NAMECITE{Side}{% Banoczi:1998:LIR% }. \NAMECITE{Signal}{% Golub:1988:NAS% }. \NAMECITE{Singular}{% Boutsikas:2024:SSV,% Chandrasekaran:1994:BEE,% Chandrasekaran:1994:DCA,% Chandrasekaran:1994:SVD,% Chandrasekaran:1995:AQA,% Drineas:2019:LRM,% Eisenstat:1993:RPT,% Eisenstat:1994:RPB,% Eisenstat:1995:RPT,% Ipsen:1984:SVD,% Chandrasekaran:1995:AAC,% Ipsen:1998:RPR% }. \NAMECITE{sketched}{% Chi:2022:PBA% }. \NAMECITE{Small}{% Boutsikas:2024:SSV% }. \NAMECITE{Snowbird}{% Lewis:1994:ALA% }. \NAMECITE{Society}{% Ipsen:2009:SID% }. \NAMECITE{Solution}{% Banoczi:1998:LIR,% Barlow:1987:SGR,% Campbell:1995:CES,% Chandrasekaran:1995:SSC,% Delosme:1986:PSS,% Delosme:1987:ESA,% Ipsen:1984:CDL,% Ipsen:1985:IPA,% Ipsen:1986:CDL,% Ipsen:1986:IPA,% Ipsen:1987:SAP,% Ipsen:1988:SAP,% Ipsen:1996:HWC,% Campbell:1996:CES,% Ipsen:2006:SIA,% Ipsen:2006:SIP,% Ipsen:2009:SIA% }. \NAMECITE{solvers}{% Bartels:2019:PLS% }. \NAMECITE{Solving}{% Ipsen:1987:SST,% Ipsen:1990:SST,% Ipsen:1987:TMS% }. \NAMECITE{Some}{% Ipsen:1990:SRG,% Ipsen:1991:SRG% }. \NAMECITE{Spaces}{% Drineas:2018:SCR% }. \NAMECITE{Special}{% Ipsen:2006:SIA,% Ipsen:2006:SIP,% Ipsen:2008:PCS,% Ipsen:2009:SIA,% Ipsen:2009:SID,% Girolami:2019:ESE,% Ipsen:2007:PCS% }. \NAMECITE{Spotlights}{% Ipsen:2012:RS% }. \NAMECITE{Squares}{% Barlow:1987:SGR,% Ipsen:2011:RDN,% Ipsen:2014:ECS% }. \NAMECITE{Stability}{% Ipsen:1994:USM% }. \NAMECITE{Stable}{% Delosme:1989:BAS,% Ipsen:1983:SMC% }. \NAMECITE{Statistical}{% Reid:2023:SPB% }. \NAMECITE{Structural}{% Drineas:2018:SCR% }. \NAMECITE{Study}{% Golub:1988:NAS% }. \NAMECITE{Subset}{% Ipsen:2011:RDN% }. \NAMECITE{Subspace}{% Holodnak:2018:PSB% }. \NAMECITE{Subspaces}{% Drineas:2018:SCR,% Eisenstat:1994:RPB,% Holodnak:2018:PSB,% Ipsen:1995:ABC,% Ipsen:2000:ARP,% Ipsen:2000:ORT,% Ipsen:2010:EIS% }. \NAMECITE{summation}{% Hallman:2023:PAD% }. \NAMECITE{Symmetric}{% Delosme:1986:PSS,% Hallman:2023:MCM,% Ipsen:1987:SAP,% Ipsen:1987:SST,% Ipsen:1988:SAP,% Ipsen:1990:SST,% Ipsen:1987:TMS% }. \NAMECITE{synthesis}{% Delosme:1986:SAS% }. \NAMECITE{System}{% Banoczi:1998:LIR,% Ipsen:1984:CDL,% Ipsen:1986:CDL% }. \NAMECITE{Systems}{% Chandrasekaran:1995:SSC,% Cockayne:2021:PIM,% Delosme:1986:PSS,% Delosme:1987:ESA,% Ipsen:1987:SAP,% Ipsen:1988:SAP% }. \NAMECITE{Systolic}{% Barlow:1987:SGR,% Delosme:1986:SAS,% Delosme:1987:ESA,% Heller:1982:SNO,% Heller:1983:SNO,% Ipsen:1984:SVD,% Ipsen:1987:SAP,% Ipsen:1988:SAP% }. \NAMECITE{Techniques}{% Eisenstat:1993:RPT,% Eisenstat:1995:RPT,% Ipsen:2005:PT,% Ipsen:2006:PTa,% Ipsen:2006:PTb,% Ipsen:2006:PTc,% Ipsen:2006:PTd,% Ipsen:2007:PTa,% Ipsen:2007:PTb,% Ipsen:2007:PTc,% Ipsen:2007:PTd,% Ipsen:2008:PTa,% Ipsen:2008:PTd,% Ipsen:2009:PTI,% Ipsen:2009:PTa,% Ipsen:2009:PTb,% Ipsen:2009:PTc,% Ipsen:2007:PT,% Ipsen:2008:PTIa,% Ipsen:2008:PTIb% }. \NAMECITE{Their}{% Heller:1982:SNO% }. \NAMECITE{theorems}{% Ipsen:2000:ORT% }. \NAMECITE{theory}{% Ipsen:2010:EIS% }. \NAMECITE{Third}{% Rodrigue:1989:PPS% }. \NAMECITE{Three}{% Eisenstat:1998:TAP,% Eisenstat:1999:TAP% }. \NAMECITE{time}{% Delosme:1986:SAS% }. \NAMECITE{{Toeplitz}}{% Delosme:1987:ESA,% Ipsen:1987:SAP,% Ipsen:1988:SAP% }. \NAMECITE{total}{% Chi:2022:PBA% }. \NAMECITE{trace}{% Saibaba:2017:RMF% }. \NAMECITE{Transformations}{% Heller:1982:SNO% }. \NAMECITE{Trees}{% Bhatt:1985:HET% }. \NAMECITE{Triangular}{% Chandrasekaran:1994:SVD% }. \NAMECITE{Tridiagonal}{% Ipsen:1987:SST,% Ipsen:1990:SST,% Ipsen:1987:TMS% }. \NAMECITE{Two}{% Ipsen:1987:TMS% }. \NAMECITE{uncertainties}{% Chi:2022:PBA% }. \NAMECITE{Uniform}{% Delosme:1990:PCA,% Gropp:1989:GCS,% Ipsen:1994:USM% }. \NAMECITE{unifying}{% Bartels:2019:PLS,% Ipsen:2003:NUA% }. \NAMECITE{Untitled}{% Ipsen:2007:U,% Ipsen:2012:U% }. \NAMECITE{Updates}{% Beckermann:2018:LRU% }. \NAMECITE{Updating}{% Ipsen:2005:CAP,% Ipsen:2006:CAP% }. \NAMECITE{Using}{% Ipsen:1984:PMU% }. \NAMECITE{Utah}{% Lewis:1994:ALA% }. \NAMECITE{Value}{% Chandrasekaran:1994:BEE,% Chandrasekaran:1994:SVD,% Drineas:2019:LRM,% Eisenstat:1993:RPT,% Eisenstat:1995:RPT,% Ipsen:1984:SVD% }. \NAMECITE{Values}{% Boutsikas:2024:SSV,% Chandrasekaran:1994:DCA,% Chandrasekaran:1995:AQA,% Chandrasekaran:1995:AAC,% Ipsen:1998:RPR% }. \NAMECITE{Vector}{% Eisenstat:1994:RPB,% Ipsen:2011:ECD% }. \NAMECITE{view}{% Bartels:2019:PLS% }. \NAMECITE{{VLSI}}{% Delosme:1987:ESA,% Ipsen:1983:SMC% }. \NAMECITE{{Wielandt}}{% Ipsen:1996:HWC% }. \NAMECITE{Workshop}{% Cullum:1986:LSE,% Ipsen:2006:SIP% }.