swMATH ID: 13371
Software Authors: Christopher C. Paige, Michael A. Saunders, Sou-Cheng Choi, Dominique Orban, Umberto Emanuele Villa, Danielle Maddix
Description: Implementation of a conjugate-gradient type method for solving sparse linear equations: Solve Ax=b or (A−sI)x=b. The matrix A−sI must be symmetric but it may be definite or indefinite or singular. The scalar s is a shifting parameter – it may be any number. The method is based on Lanczos tridiagonalization. You may provide a preconditioner, but it must be positive definite. MINRES is really solving one of the least-squares problems minimize ||Ax−b|| or ||(A−sI)x−b||. If A is singular (and s=0), MINRES returns a least-squares solution with small ||Ar|| (where r=b−Ax), but in general it is not the minimum-length solution. To get the min-length solution, use MINRES-QLP [2,3]. Similarly if A−sI is singular.
Homepage: http://web.stanford.edu/group/SOL/software/minres/
Related Software: MINRES-QLP; LSQR; SparseMatrix; LSMR; CUTEst; MUMPS; CGS; mctoolbox; PETSc; SLEPc; Ipopt; ARPACK; Gurobi; Matlab; LAPACK; Julia; Adam; AdaGrad; L-BFGS; JDQZ
Referenced in: 41 Publications
all top 5

Referenced by 80 Authors

7 Orban, Dominique
6 Saunders, Michael A.
5 Paige, Christopher C.
3 Estrin, Ron
2 Choi, Sou-Cheng T.
2 Lim, Lek-Heng
2 Montoison, Alexis
2 Titley-Péloquin, David
1 Al-Baali, Mehiddin
1 Athènes, Manuel
1 Bergou, El Houcine
1 Bouchard, Kristofer E.
1 Caliciotti, Andrea
1 Chang, Xiaowen
1 Chen, Qiao
1 Claeys, Xavier
1 Creuze, Jérôme
1 Cui, Tiangang
1 Curtis, Frank E.
1 Dahito, Marie-Ange
1 Dai, Hua
1 DeWeese, Michael R.
1 Diouane, Youssef
1 Dostál, Zdeněk
1 Duintjer Tebbens, Jurjen
1 Fasano, Giovanni
1 Frye, Charles G.
1 Giacomel, Lorenzo
1 Gondzio, Jacek
1 Goulart, Paul J.
1 Gould, Nick I. M.
1 Greif, Chen
1 Hallman, Eric
1 He, Qinglong
1 He, Ying
1 Hiptmair, Ralf
1 Il’in, Valeriĭ Pavlovich
1 Jiang, Xiaoye
1 Jiao, Xiangmin
1 Kalantzis, Vassilis
1 Kaur, Savneet
1 Knyazev, Andrew V.
1 Kungurtsev, Vyacheslav
1 Lauwens, Ben
1 Ligeralde, Andrew
1 Liu, Yang
1 Manguoglu, Murat
1 Marzouk, Youssef M.
1 Mehrmann, Volker
1 Meurant, Gérard A.
1 Moré, Jorge J.
1 Nakatsukasa, Yuji
1 Nocedal, Jorge
1 Olshanskii, Maxim A.
1 Petit, Julien
1 Pospíšil, Lukáš
1 Potschka, Andreas
1 Rees, Tyrone
1 Roma, Massimo
1 Rontsis, Nikitas
1 Roosta, Fred
1 Royer, Clément W.
1 Schork, Lukas
1 Simon, James
1 Simoncini, Valeria
1 Spantini, Alessio
1 Tenorio, Luis
1 Trinath, G.
1 Urzúa-Torres, Carolina
1 Varah, James M.
1 Vecharynski, Eugene
1 Wächter, Andreas
1 Wadia, Neha S.
1 Wang, Yanfei
1 Wild, Stefan M.
1 Willcox, Karen E.
1 Yao, Yuan
1 Ye, Yinyu
1 Zhang, Jianhua
1 Zuo, Qian

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