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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: Regularization tools; LSMR; SparseMatrix; UTV; mctoolbox; Matlab; MINRES; IR Tools; AIR tools; RestoreTools; HSL; CGS; JDQZ; LAPACK; GKB-FP; CUTEst; JDQR; ErresTools; LSRN; PDCO
Cited in: 415 Publications
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Cited by 644 Authors

23 Reichel, Lothar
15 Saunders, Michael A.
11 Jia, Zhongxiao
8 Chung, Julianne M.
8 Orban, Dominique
8 Van der Vorst, Henk Albertus
7 Jbilou, Khalide
7 Paige, Christopher C.
7 Ravnik, Jure
6 Boyd, Stephen Poythress
6 Calvetti, Daniela
6 Golub, Gene Howard
6 Karimi, Saeed
6 Scott, Jennifer A.
6 Strakoš, Zdeněk
6 Titley-Péloquin, David
6 Viloche Bazán, Fermín S.
5 Gazzola, Silvia
5 Morigi, Serena
5 Morikuni, Keiichi
5 Nagy, James Gerard
5 Novati, Paolo
5 Sadok, Hassane
5 Sgallari, Fiorella
5 Wathen, Andrew John
4 Barlow, Jesse L.
4 Bentbib, Abdeslem Hafid
4 Borges, Leonardo Silveira
4 Bouhamidi, Abderrahman
4 Chung, Matthias
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 Renaut, Rosemary Anne
4 Rodriguez, Giuseppe
4 Tenorio, Luis
4 Toutounian, Faezeh
4 Wang, Minghui
4 Žunič, Zoran
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 Lukšan, Ladislav
3 Majander, H.
3 Potts, Daniel
3 Schmischke, Michael
3 Škerget, Leopold
3 Somersalo, Erkki
3 Tichý, Petr
3 Toint, Philippe L.
3 Tůma, Miroslav
3 Ullrich, Tino
3 Vuik, Cornelis
2 Al-Homidan, Suliman S.
2 Andreev, Roman
2 Austen, Gerrit
2 Avron, Haim
2 Baglama, James
2 Baur, Oliver
2 Beik, Fatemeh Panjeh Ali
2 Bierlaire, Michel
2 Björck, Åke
2 Boelens, Arnout M. P.
2 Chen, Scott Shaobing
2 Choi, Sou-Cheng T.
2 Cornelis, Jeffrey
2 Cui, Tiangang
2 Cunha, Maria Cristina C.
2 Dierckx, Paul
2 Donoho, David Leigh
2 El-Guide, Mohamed
2 Entezami, Alireza
2 Ferreira, Orizon Pereira
2 Gill, Philip E.
2 Goldfarb, Donald
2 Gondzio, Jacek
2 González-Lima, María D.
2 Greif, Chen
2 Gröchenig, Karlheinz
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2 Harker, Matthew
2 Herrmann, Felix J.
2 Hriberšek, Matjaž
2 Hyndman, Rob J.
2 Jia, Zhigang
2 Khouia, Asmaa
2 Knepper, Sarah
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Cited in 107 Serials

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16 Journal of Computational Physics
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7 SIAM Review
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4 ACM Transactions on Mathematical Software
4 Computers & Operations Research
4 Applied Mathematical Modelling
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3 International Journal for Numerical Methods in Engineering
3 Annals of Operations Research
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3 Journal of Applied Mathematics and Computing
3 SIAM Journal on Imaging Sciences
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2 International Journal of Computer Mathematics
2 SIAM Journal on Optimization
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2 Computational and Applied Mathematics
2 Advances in Computational Mathematics
2 Mathematical Problems in Engineering
2 Foundations of Computational Mathematics
2 Inverse Problems and Imaging
2 Mathematical Geosciences
2 GEM - International Journal on Geomathematics
2 Journal of Applied Mathematics & Informatics
1 Applicable Analysis
1 Computers and Fluids
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1 Journal of Engineering Mathematics
1 Journal of Mathematical Physics
1 Linear and Multilinear Algebra
1 Mathematical Methods in the Applied Sciences
1 Physica A
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1 Mathematics and Computers in Simulation
1 Mathematical Programming
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1 SIAM Journal on Algebraic and Discrete Methods
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