MINRES-QLP
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.
This software is also peer reviewed by journal TOMS.
This software is also peer reviewed by journal TOMS.
Keywords for this software
References in zbMATH (referenced in 8 articles , 2 standard articles )
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Sorted by year (- Duintjer Tebbens, Jurjen; Meurant, Gérard: On the convergence of Q-OR and Q-MR Krylov methods for solving nonsymmetric linear systems (2016)
- Vecharynski, Eugene; Knyazev, Andrew: Preconditioned steepest descent-like methods for symmetric indefinite systems (2016)
- Zhang, Jianhua; Dai, Hua: A transpose-free quasi-minimal residual variant of the CORS method for solving non-Hermitian linear systems (2015)
- Choi, Sou-Cheng T.; Saunders, Michael A.: Algorithm 937: MINRES-QLP for symmetric and Hermitian linear equations and least-squares problems (2014)
- Moré, Jorge J.; Wild, Stefan M.: Do you trust derivatives or differences? (2014)
- Choi, Sou-Cheng T.; Paige, Christopher C.; Saunders, Michael A.: MINRES-QLP: a Krylov subspace method for indefinite or singular symmetric systems (2011)
- Jiang, Xiaoye; Lim, Lek-Heng; Yao, Yuan; Ye, Yinyu: Statistical ranking and combinatorial Hodge theory (2011)
- Choi, Sou-Cheng T.; Paige, Christopher C.; Saunders, Michael A.: MINRES-QLP: a Krylov subspace method for indefinite or singular symmetric systems (2010) ioport