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LSMR

swMATH ID: 12940
Software Authors: Fong, David Chin-Lung; Saunders, Michael
Description: LSMR: an iterative algorithm for sparse least-squares problems. An iterative method LSMR is presented for solving linear systems Ax=b and least-squares problems min∥Ax-b∥ 2 , with A being sparse or a fast linear operator. LSMR is based on the Golub-Kahan bidiagonalization process. It is analytically equivalent to the MINRES method applied to the normal equation A T Ax=A T b, so that the quantities ∥A T r k ∥ are monotonically decreasing (where r k =b-Ax k is the residual for the current iterate x k ). We observe in practice that ∥r k ∥ also decreases monotonically, so that compared to LSQR (for which only ∥r k ∥ is monotonic) it is safer to terminate LSMR early. We also report some experiments with reorthogonalization.
Homepage: http://web.stanford.edu/group/SOL/software/lsmr/
Keywords: least-squares problem; sparse matrix; LSQR; MINRES; Krylov subspace method; golub-kahan process; conjugate-gradient method; minimum-residual method; iterative method
Related Software: LSQR; SparseMatrix; Regularization tools; MINRES; UTV; RestoreTools; CUTEst; mctoolbox; Matlab; IR Tools; MINRES-QLP; SuiteSparseQR; GitHub; MIQR; AIR tools; GKB-FP; HSL; HSL_MI28; MA57; LSRN
Cited in: 75 Publications
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Cited by 156 Authors

6 Orban, Dominique
5 Titley-Péloquin, David
4 Chung, Julianne M.
4 Scott, Jennifer A.
3 Gazzola, Silvia
3 Jia, Zhongxiao
3 Mojarrab, Maryam
3 Morikuni, Keiichi
3 Paige, Christopher C.
3 Saunders, Michael A.
3 Toutounian, Faezeh
2 Avron, Haim
2 Baglama, James
2 Chang, Xiaowen
2 Deng, Liangjian
2 Estrin, Ron
2 Greif, Chen
2 Hayami, Ken
2 Huang, Ting-Zhu
2 Kilmer, Misha Elena
2 Liu, Xiaoxing
2 Morita, Koji
2 Richmond, Daniel J.
2 Tůma, Miroslav
2 Zhang, Shuai
2 Zhao, Xile
1 Ahmadi-Asl, Salman
1 Ardestani, Vahid E.
1 Arreckx, Sylvain
1 Arridge, Simon R.
1 Asgari, Zohreh
1 Beik, Fatemeh Panjeh Ali
1 Bellavia, Stefania
1 Benson, Austin R.
1 Betcke, Marta M.
1 Bock, Hans Georg
1 Boyd, Stephen Poythress
1 Buttari, Alfredo
1 Cancino Chacón, Carlos Eduardo
1 Cao, Jian
1 Cerdán, Juana
1 Chen, Qiao
1 Cheng, Li
1 Cheng, Xuehan
1 Choi, Sou-Cheng T.
1 Chu, Delin
1 Coletti, Filippo
1 Conder, James A.
1 Coppé, Vincent
1 Crocher, Vincent
1 Cui, Tiangang
1 Dahito, Marie-Ange
1 Davis, Timothy Alden
1 Deadman, Edvin
1 Diamond, Steven
1 Doan, Xuan Vinh
1 Druinsky, Alex
1 Eaton, John K.
1 Entezami, Alireza
1 Fong, David Chin-Lung
1 Fong, Justin
1 Foster, Leslie V.
1 Gadermaier, Thassilo
1 Garcés, María Elena Suaréz
1 Gondzio, Jacek
1 Gong, Maoguo
1 Gould, Nicholas Ian Mark
1 Gould, Nick I. M.
1 Grachten, Maarten
1 Gratton, Serge
1 Gu, Xian-Ming
1 Gutekunst, Jürgen
1 Hallman, Eric
1 Harhanen, Lauri
1 Hasanpour, Afsaneh
1 Heinisch, Philip
1 Herrmann, Felix J.
1 Higham, Nicholas J.
1 Hnětynková, Iveta
1 Hochstenbach, Michiel E.
1 Holman, Sean F.
1 Horn, Paul S.
1 Huang, Baohua
1 Huybrechs, Daan
1 Iaccarino, Gianluca
1 Jadbabaie, Ali
1 Ji, Hao
1 Jiang, Xiangming
1 Jiao, Xiangmin
1 Jiránek, Pavel
1 Jozi, Meisam
1 Kang, Peng
1 Karamodin, Abbas
1 Karimi, Saeed
1 Khojasteh Salkuyeh, Davod
1 Kruk, Serge G.
1 Kubínová, Marie
1 Li, Yaohang
1 Li, Zhengming
1 Liao, Li-Zhi
...and 56 more Authors

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