MINRES-QLP swMATH ID: 11181 Software Authors: Choi, Sou-Cheng T.; Saunders, Michael A. Description: Algorithm 937: MINRES-QLP for symmetric and Hermitian linear equations and least-squares problems. We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-definite preconditioner may be supplied. Our FORTRAN 90 implementation illustrates a design pattern that allows users to make problem data known to the solver but hidden and secure from other program units. In particular, we circumvent the need for reverse communication. Example test programs input and solve real or complex problems specified in Matrix Market format. While we focus here on a FORTRAN 90 implementation, we also provide and maintain MATLAB versions of MINRES and MINRES-QLP. Homepage: http://dl.acm.org/citation.cfm?doid=2594412.2527267 Keywords: Krylov subspace method; Lanczos process; conjugate-gradient method; data encapsulation; ill-posed problem; linear equations; minimum-residual method; pseudoinverse solution; regression; singular least-squares; sparse matrix Related Software: MINRES; SparseMatrix; LSQR; LSMR; Matlab; ARPACK; MUMPS; LAPACK; CGS; PETSc; SLEPc; CUTEst; Julia; Adam; AdaGrad; PRIMME; FEAST; L-BFGS; mctoolbox; GAIL Cited in: 26 Publications Standard Articles 2 Publications describing the Software, including 2 Publications in zbMATH Year Algorithm 937: MINRES-QLP for symmetric and Hermitian linear equations and least-squares problems. Zbl 1305.65117Choi, Sou-Cheng T.; Saunders, Michael A. 2014 MINRES-QLP: a Krylov subspace method for indefinite or singular symmetric systems. Zbl 1230.65050Choi, Sou-Cheng T.; Paige, Christopher C.; Saunders, Michael A. 2011 all top 5 Cited by 54 Authors 2 Choi, Sou-Cheng T. 2 Lim, Lek-Heng 2 Montoison, Alexis 2 Orban, Dominique 2 Paige, Christopher C. 2 Saunders, Michael A. 1 Al-Baali, Mehiddin 1 Athènes, Manuel 1 Avron, Haim 1 Bergou, El Houcine 1 Bouchard, Kristofer E. 1 Caliciotti, Andrea 1 Chen, Qiao 1 Creuze, Jérôme 1 Dai, Hua 1 DeWeese, Michael R. 1 Diouane, Youssef 1 Dostál, Zdeněk 1 Druinsky, Alex 1 Duintjer Tebbens, Jurjen 1 Fasano, Giovanni 1 Frye, Charles G. 1 Goulart, Paul J. 1 He, Qinglong 1 He, Ying 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 Lieder, Felix 1 Ligeralde, Andrew 1 Manguoglu, Murat 1 Mehrmann, Volker 1 Meurant, Gérard A. 1 Moré, Jorge J. 1 Nakatsukasa, Yuji 1 Pospíšil, Lukáš 1 Roma, Massimo 1 Rontsis, Nikitas 1 Roosta, Fred 1 Royer, Clément W. 1 Simon, James 1 Toledo, Sivan 1 Vecharynski, Eugene 1 Wadia, Neha S. 1 Wang, Yanfei 1 Wild, Stefan M. 1 Yao, Yuan 1 Ye, Yinyu 1 Zhang, Jianhua 1 Zuo, Qian all top 5 Cited in 15 Serials 5 SIAM Journal on Scientific Computing 3 Journal of Computational Physics 3 SIAM Journal on Matrix Analysis and Applications 3 SIAM Journal on Optimization 2 Mathematical Programming. Series A. Series B 1 Inverse Problems 1 ACM Transactions on Mathematical Software 1 BIT 1 Neural Computation 1 International Journal of Computer Mathematics 1 Linear Algebra and its Applications 1 SIAM Review 1 Numerical Linear Algebra with Applications 1 Computational and Applied Mathematics 1 Doklady Mathematics all top 5 Cited in 13 Fields 22 Numerical analysis (65-XX) 7 Operations research, mathematical programming (90-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Computer science (68-XX) 1 Combinatorics (05-XX) 1 Group theory and generalizations (20-XX) 1 Integral transforms, operational calculus (44-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Statistics (62-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX) Citations by Year