GMRES implementations and residual smoothing techniques for solving ill-posed linear systems

Matinfar, M.; Zareamoghaddam, H.; Eslami, Mostafa; Saeidy, M.

doi:10.1016/j.camwa.2011.09.022

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Convergence Behavior1

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Cited by 16 publications

(2 citation statements)

References 30 publications

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“…In 2006, it was proved by Paige et al [204] that MGS-GMRES is also backward stable; previous observations can be found in [127,206]. Due to the ill-conditioning of the matrix Z n in (12), SGMRES has serious stability problems (see, e.g, [164,56]), which can be partially remedied by using RB-SGMRES [150] or the adaptive variant (14) [149]; see also the experiments in [180].…”

Section: Convergence Behaviormentioning

confidence: 97%

GMRES algorithms over 35 years

Zou

2021

Preprint

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Section: Convergence Behaviormentioning

confidence: 97%

GMRES algorithms over 35 years

Zou

2021

Preprint

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“…Matinfar et al [19] illustrate the application of several GMRES-type methods to the solution of Tikhonov regularized linear discrete ill-posed problems,…”

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confidence: 99%

Some properties of range restricted GMRES methods

Bellalij

Reichel

Sadok

2015

Journal of Computational and Applied Mathematics

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The GMRES method is one of the most popular iterative schemes for the solution of large linear systems of equations with a square nonsingular matrix. GMRES-type methods also have been applied to the solution of linear discrete ill-posed problems. Computational experience indicates that for the latter problems, variants of the standard GMRES method, that require the solution to live in the range of a positive power of the matrix of the linear system of equations to be solved, generally yield more accurate approximations of the desired solution than standard GMRES. This paper investigates properties of these variants of GMRES.

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