Using successive approximations for improving the convergence of GMRES method
type: Item
instance of: scholarly article
title: Using successive approximations for improving the convergence of GMRES method
zbMATH Open document ID: 0938.65060
DOI: 10.1023/A:1022291601664
published in: Applications of Mathematics
publication date: 2000-05-22T00:00:00Z
full work available at URL: https://eudml.org/doc/33014
review text: A possibility how to improve the convergence of the GMRES method for the iterative solution of the system \((I-T)x=b\) of linear algebraic equations with a nonsymmetric matrix is suggested. It consists in performing \(m\) pre-iterations of the form \(y_{l+1}=Ty_l+b\) before starting GMRES and in putting \(y_m\) as the initial approximation for GMRES. From the practical point of view, such pre-processing seems to be advantageous since one iteration of the pre-processing process costs less work that one of GMRES. Numerical tests confirm this hypothesis and the theory presented in the paper explains this observations.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N35
zbMATH DE Number: 1450157
zbMATH Keywords: GMRES
zbMATH Keywords: iterative method
zbMATH Keywords: numerical experiments
zbMATH Keywords: solution of dicsretized equations
author: Jan Zítko
MaRDI profile type: Publication
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OpenAlex ID: W24714695
description: scientific article; zbMATH DE number 1450157