Avoiding breakdown in Van der Vorst's method
type: Item
instance of: scholarly article
title: Avoiding breakdown in Van der Vorst's method
zbMATH Open document ID: 0956.65024
DOI: 10.1023/A:1019145010317
published in: Numerical Algorithms
publication date: 2000-09-07T00:00:00Z
review text: The purpose of this paper is to overcome the breakdown of convergence for the Lanczos iterative method and also for \textit{H. A. Van der Vorst} method [SIAM J. Sci. Stat. Comput. 13, No. 2, 631-644 (1992; Zbl 0761.65023)] applied to large sparse linear systems. The authors develop a polynomial method which defines the iterates for the approximate solution of the linear system as quotients of some polynomials having the coefficients expressed in terms of an associated sequence. Numerical examples show that the described algorithm seems to be much more robust than the Lanczos iteration.
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 1382964
zbMATH Keywords: large sparse linear system
zbMATH Keywords: non-Hermitian matrix
zbMATH Keywords: Lanczos iterative method
zbMATH Keywords: avoiding breakdown
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
zbMATH Keywords: algorithm
author: Peter R. Graves-Morris
author: Ahmed Salam
reviewed by: Iulian Coroian
MaRDI profile type: Publication
full work available at URL: a:1019145010317
OpenAlex ID: W166811416
description: scientific article; zbMATH DE number 1382964