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LSQR

swMATH ID: 530
Software Authors: Paige, Christopher C.; Saunders, Michael A.
Description: Algorithm 583: LSQR: Sparse Linear Equations and Least Squares Problems. An iterative method is given for solving Ax = b and min|| Ax - b||2 , where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerical properties. Reliable stopping criteria are derived, along with estimates of standard errors for x and the condition number of A. These are used in the FORTRAN implementation of the method, subroutine LSQR. Numerical tests are described comparing LSQR with several other conjugate-gradient algorithms, indicating that LSQR is the most reliable algorithm when A is ill-conditioned.
Homepage: http://dl.acm.org/citation.cfm?id=356000
Keywords: bidiagonalization; conjugate gradients; estimates of errors; numerical tests; sparse and very large systems; linear least squares
Related Software: CRAIG; Regularization tools; LSMR; SparseMatrix; UTV; mctoolbox; Matlab; IR Tools; MINRES; JDQZ; GitHub; CGS; JDQR; AIR tools; RestoreTools; HSL; LSRN; LAPACK; GKB-FP; PROPACK
Cited in: 441 Documents
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Cited by 701 Authors

24 Reichel, Lothar
17 Saunders, Michael A.
12 Jia, Zhongxiao
9 Orban, Dominique
8 Chung, Julianne M.
8 Van der Vorst, Henk Albertus
7 Jbilou, Khalide
7 Paige, Christopher C.
7 Ravnik, Jure
6 Boyd, Stephen Poythress
6 Calvetti, Daniela
6 Gazzola, Silvia
6 Golub, Gene Howard
6 Karimi, Saeed
6 Scott, Jennifer
6 Strakoš, Zdeněk
6 Titley-Péloquin, David
6 Viloche Bazán, Fermín S.
5 Chung, Matthias
5 Morigi, Serena
5 Morikuni, Keiichi
5 Nagy, James Gerard
5 Novati, Paolo
5 Renaut, Rosemary Anne
5 Sadok, Hassane
5 Sgallari, Fiorella
5 Toutounian, Faezeh
5 Wathen, Andrew John
4 Barlow, Jesse L.
4 Bentbib, Abdeslem Hafid
4 Borges, Leonardo Silveira
4 Bouhamidi, Abderrahman
4 Estrin, Ron
4 Hajarian, Masoud
4 Hansen, Per Christian
4 Hayami, Ken
4 Hnětynková, Iveta
4 Hochstenbach, Michiel E.
4 Hyvönen, Nuutti
4 Jozi, Meisam
4 Kilmer, Misha Elena
4 Ling, Sitao
4 O’Leary, Dianne P.
4 Rodriguez, Giuseppe
4 Tenorio, Luis
4 Wang, Minghui
4 Žunič, Zoran
3 Baglama, James
3 Brezinski, Claude
3 Chang, Xiaowen
3 Dongarra, Jack J.
3 Duff, Iain S.
3 Gratton, Serge
3 Hallman, Eric
3 Harhanen, Lauri
3 Huang, Ting-Zhu
3 Kolehmainen, Ville
3 Li, Haibo
3 Lukšan, Ladislav
3 Majander, H.
3 Pestana, Jennifer
3 Potts, Daniel
3 Ramšak, Matjaž
3 Saibaba, Arvind Krishna
3 Schmischke, Michael
3 Škerget, Leopold
3 Somersalo, Erkki
3 Tichý, Petr
3 Toint, Philippe Louis
3 Tůma, Miroslav
3 Ullrich, Tino
3 Vuik, Cornelis
2 Al-Homidan, Suliman S.
2 Andreev, Roman
2 Austen, Gerrit
2 Avron, Haim
2 Baur, Oliver
2 Beik, Fatemeh Panjeh Ali
2 Bierlaire, Michel
2 Björck, Åke
2 Boelens, Arnout M. P.
2 Brust, Johannes J.
2 Cen, Kefa
2 Chen, Scott Shaobing
2 Chi, Yong
2 Choi, Sou-Cheng T.
2 Cornelis, Jeffrey
2 Cui, Tiangang
2 Cunha, Maria Cristina C.
2 Dierckx, Paul
2 Donoho, David Leigh
2 Entezami, Alireza
2 Eslahchi, Mohammad Reza
2 Ferreira, Orizon Pereira
2 Gill, Philip E.
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2 Gondzio, Jacek
2 González-Lima, María D.
2 Greengard, Leslie F.
2 Greif, Chen
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Cited in 113 Serials

36 SIAM Journal on Scientific Computing
28 Journal of Computational and Applied Mathematics
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3 International Journal of Heat and Mass Transfer
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