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.

References in zbMATH (referenced in 28 articles , 2 standard articles )

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  1. Jiao, Xiangmin; Chen, Qiao: Approximate generalized inverses with iterative refinement for (\epsilon)-accurate preconditioning of singular systems (2022)
  2. Kaur, Savneet; Athènes, Manuel; Creuze, Jérôme: Absorption kinetics of vacancies by cavities in aluminum: numerical characterization of sink strengths and first-passage statistics through Krylov subspace projection and eigenvalue deflation (2022)
  3. Rontsis, Nikitas; Goulart, Paul J.; Nakatsukasa, Yuji: An active-set algorithm for norm constrained quadratic problems (2022)
  4. Bergou, El Houcine; Diouane, Youssef; Kungurtsev, Vyacheslav; Royer, Clément W.: A nonmonotone matrix-free algorithm for nonlinear equality-constrained least-squares problems (2021)
  5. Frye, Charles G.; Simon, James; Wadia, Neha S.; Ligeralde, Andrew; Deweese, Michael R.; Bouchard, Kristofer E.: Critical point-finding methods reveal gradient-flat regions of deep network losses (2021)
  6. Liu, Yang; Roosta, Fred: Convergence of Newton-MR under inexact Hessian information (2021)
  7. Montoison, Alexis; Orban, Dominique: TriCG and TriMR: two iterative methods for symmetric quasi-definite systems (2021)
  8. Al-Baali, Mehiddin; Caliciotti, Andrea; Fasano, Giovanni; Roma, Massimo: A class of approximate inverse preconditioners based on Krylov-subspace methods for large-scale nonconvex optimization (2020)
  9. He, Qinglong; Wang, Yanfei: Inexact Newton-type methods based on Lanczos orthonormal method and application for full waveform inversion (2020)
  10. Il’in, V. P.: On moment methods in Krylov subspaces (2020)
  11. Kalantzis, Vassilis: A domain decomposition Rayleigh-Ritz algorithm for symmetric generalized eigenvalue problems (2020)
  12. Lieder, Felix: Solving large-scale cubic regularization by a generalized eigenvalue problem (2020)
  13. Lim, Lek-Heng: Hodge Laplacians on graphs (2020)
  14. Montoison, Alexis; Orban, Dominique: BiLQ: an iterative method for nonsymmetric linear systems with a quasi-minimum error property (2020)
  15. Zuo, Qian; He, Ying: Preconditioned GMRES method for a class of Toeplitz linear systems in fractional eigenvalue problems (2020)
  16. Avron, Haim; Druinsky, Alex; Toledo, Sivan: Spectral condition-number estimation of large sparse matrices. (2019)
  17. Manguoğlu, Murat; Mehrmann, Volker: A robust iterative scheme for symmetric indefinite systems (2019)
  18. Paige, Christopher C.: Accuracy of the Lanczos process for the eigenproblem and solution of equations (2019)
  19. Dostál, Zdeněk; Pospíšil, Lukáš: Conjugate gradients for symmetric positive semidefinite least-squares problems (2018)
  20. Duintjer Tebbens, Jurjen; Meurant, Gérard: On the convergence of Q-OR and Q-MR Krylov methods for solving nonsymmetric linear systems (2016)

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