Residual-based simpler block GMRES for nonsymmetric linear systems with multiple right-hand sides
type: Item
instance of: scholarly article
title: Residual-based simpler block GMRES for nonsymmetric linear systems with multiple right-hand sides
zbMATH Open document ID: 1431.65037
DOI: 10.1155/2018/1369707
author: Qinghua Wu
author: Liang Bao
author: Yiqin Lin
published in: Advances in Mathematical Physics
publication date: 2018-12-11T00:00:00Z
review text: Summary: We propose in this paper a residual-based simpler block GMRES method for solving a system of linear algebraic equations with multiple right-hand sides. We show that this method is mathematically equivalent to the block GMRES method and thus equivalent to the simpler block GMRES method. Moreover, it is shown that the residual-based method is numerically more stable than the simpler block GMRES method. Based on the deflation strategy proposed by \textit{H. Calandra} et al. [SIAM J. Sci. Comput. 35, No. 5, S345--S367 (2013; Zbl 1281.65056)], we derive a deflation strategy to detect the possible linear dependence of the residuals and a near rank deficiency occurring in the block Arnoldi procedure. Numerical experiments are conducted to illustrate the performance of the new method.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F25
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 6991920
zbMATH Keywords: block GMRES method
zbMATH Keywords: multiple right-hand sides
zbMATH Keywords: residual-based methods
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/1369707
OpenAlex ID: W2801508101
cites work: Parallel iterative methods for sparse linear systems
cites work: GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
cites work: An Iterative Method for Nonsymmetric Systems with Multiple Right-Hand Sides
cites work: Convergence properties of block GMRES and matrix polynomials
cites work: Exact and inexact breakdowns in the block GMRES method
cites work: A modified block flexible GMRES method with deflation at each iteration for the solution of non-Hermitian linear systems with multiple right-hand sides
cites work: Simpler block GMRES for nonsymmetric systems with multiple right-hand sides
cites work: How to Make Simpler GMRES and GCR More Stable
cites work: A simpler GMRES
Recommended article: Simpler block GMRES for nonsymmetric systems with multiple right-hand sides
Recommended article: A hybrid block GMRES method for nonsymmetric systems with multiple right-hand sides
Recommended article: Global simpler GMRES for nonsymmetric systems with multiple right-hand sides
Recommended article: A flexible and adaptive simpler block GMRES with deflated restarting for linear systems with multiple right-hand sides
Recommended article: A Weighted Block GMRES method for solving linear systems with multiple right-hand sides
Recommended article: A block varaint of the GMRES method for unsymmetric linear systems
Recommended article: Q3004851
Recommended article: GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
Recommended article: A new shifted block GMRES method with inexact breakdowns for solving multi-shifted and multiple right-hand sides linear systems
Recommended article: A block GMRES method with deflated restarting for solving linear systems with multiple shifts and multiple right‐hand sides
description: scientific article; zbMATH DE number 6991920