A note on the convergence behavior of GMRES
type: Item
instance of: scholarly article
title: A note on the convergence behavior of GMRES
zbMATH Open document ID: 0884.65025
DOI: 10.1016/S0168-9274(97)00039-1
published in: Applied Numerical Mathematics
publication date: 1998-04-02T00:00:00Z
review text: The purpose of this note is to generalize the results on the convergence behaviour of the generalized minimal residual (GMRES) method for solving symmetric linear systems [cf. \textit{Y. Saad} and \textit{M. H. Schultz}, SIAM J. Sci. Stat. Comput. 7, 856-869 (1986; Zbl 0599.65018)]. A number of theorems is presented but no numerical result is carried out.
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 1072311
zbMATH Keywords: GMRES
zbMATH Keywords: generalized minimal residual method
zbMATH Keywords: convergence
zbMATH Keywords: symmetric linear systems
author: Zhi-Hao Cao
reviewed by: Prabhat Kumar Mahanti
MaRDI profile type: Publication
cites work: A Theoretical Comparison of the Arnoldi and GMRES Algorithms
cites work: Peaks, plateaus, numerical instabilities in a Galerkin minimal residual pair of methods for solving \(Ax=b\)
cites work: Relations between Galerkin and Norm-Minimizing Iterative Methods for Solving Linear Systems
cites work: Quasi-kernel polynomials and their use in non-Hermitian matrix iterations
cites work: On the roots of the orthogonal polynomials and residual polynomials associated with a conjugate gradient method
cites work: On hybrid iterative methods for nonsymmetric systems of linear equations
cites work: Approximate solutions and eigenvalue bounds from Krylov subspaces
cites work: GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
cites work: The rate of convergence of conjugate gradients
cites work: The superlinear convergence behaviour of GMRES
full work available at URL: s0168-9274(97)00039-1
OpenAlex ID: W2006753818
description: scientific article; zbMATH DE number 1072311