Codes

Range-symmetric linear system solvers

Matlab codes

• GMRES, RRGMRES, RSMAR, DGMRES, MINRES-QLP, MINARES, mar.mlx

References

• Kui Du, Jia-Jun Fan, and Fang Wang, Obtaining the pseudoinverse solution of singular range-symmetric linear systems with GMRES-type methods, arXiv:2401.11788, 2024.

• Alexis Montoison, Dominique Orban, and Michael A. Saunders, MINARES: An iterative solver for symmetric linear systems, arXiv:2310.01757, 2023.

• Arthur Neuman, Lothar Reichel, and Hassane Sadok, Algorithms for range restricted iterative methods for linear discrete ill-posed problems, NA, 2012

• Sou-Cheng T. Choi, Christopher C. Paige, and Michael A. Saunders, MINRES-QLP: A Krylov subspace method for indefinite or singular symmetric systems, SISC, 2011

• Avram Sidi, DGMRES: A GMRES-type algorithm for Drazin-inverse solution of singular nonsymmetric linear systems, LAA, 2001

• Homer F. Walker and Lu Zhou, A simpler GMRES, NLAA, 1994

• Youcef Saad and Martin H. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SISSC, 1986

Partitioned linear system solvers

Matlab codes

• GPBiLQ, GPQMR, GPMR, TriCG, TriMR, gp.mlx

References

• Kui Du, Jia-Jun Fan, and Fang Wang, GPBiLQ and GPQMR: Two iterative methods for unsymmetric partitioned linear systems, arXiv:2401.02608, 2024.

• Alexis Montoison and Dominique Orban, Krylov.jl: A Julia basket of hand-picked Krylov methods, JOSS, 2023. Krylov.jl documentation

• Alexis Montoison and Dominique Orban, GPMR: An iterative method for unsymmetric partitioned linear systems, SIMAX, 2023.

• Alexis Montoison and Dominique Orban, TriCG and TriMR: Two iterative methods for symmetric quasi-definite systems, SISC, 2021.

Regularized randomized iterative algorithms

Matlab codes

• RK-RK, RK-RSK, RGS-RK, RGS-RSK, RSK, GERK-(a,d)

References

• Kui Du, Regularized randomized iterative algorithms for factorized linear systems, AMC, 2024

• Frank Schöpfer, Dirk A. Lorenz, Lionel Tondji, and Maximilian Winkler, Extended randomized Kaczmarz method for sparse least squares and impulsive noise problems, LAA, 2022

Admissible harmonic Ritz value set for GMRES

Matlab codes

• Generating matrices and initial vectors with arbitrary harmonic Ritz values and residual norms for GMRES, Jurjen Duintjer Tebbens, 10.2.2017

Reference

• Kui Du, Jurjen Duintjer Tebbens, and Gérard Meurant, Any admissible harmonic Ritz value set is possible for GMRES, ETNA, 2017.