Nested Krylov methods based on GCR
type: Item
instance of: scholarly article
title: Nested Krylov methods based on GCR
zbMATH Open document ID: 0854.65026
DOI: 10.1016/0377-0427(94)00123-5
published in: Journal of Computational and Applied Mathematics
publication date: 1997-01-26T00:00:00Z
review text: The author presents an extension of the GMRESR method for the solution of systems of linear equations where the orthogonality relations of the outer method GCR are preserved in the inner method GMRES\((m)\). At the end of the inner iteration the error is minimized over the space spanned by the search vectors both in the outer method and the inner method. This leads to optimal corrections to the solution in the outer method. Besides a detailed discussion of optimality, the possibility of breakdown and the continuation after breakdown implementation issues (including truncation in the outer method and the usage of BiCGStab instead of GMRES\((m)\) as inner method) are considered. Furthermore, several numerical examples are discussed.
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 908353
zbMATH Keywords: Krylov methods
zbMATH Keywords: inner/outer methods
zbMATH Keywords: GMRESR method
zbMATH Keywords: orthogonality relations
zbMATH Keywords: numerical examples
author: E. de Sturler
reviewed by: Andreas Frommer
describes a project that uses: CGS
describes a project that uses: ILUT
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)00123-5
OpenAlex ID: W2122830560
cites work: A Black Box Generalized Conjugate Gradient Solver with Inner Iterations and Variable-Step Preconditioning
cites work: Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
cites work: Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method
cites work: Q4091368
cites work: QMR: A quasi-minimal residual method for non-Hermitian linear systems
cites work: An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
cites work: ILUT: A dual threshold incomplete LU factorization
cites work: A Flexible Inner-Outer Preconditioned GMRES Algorithm
cites work: GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
cites work: BiCGstab(\(l\)) for linear equations involving unsymmetric matrices with complex spectrum
cites work: CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
cites work: Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
cites work: GMRESR: a family of nested GMRES methods
description: scientific article; zbMATH DE number 908353