Arnoldi versus nonsymmetric Lanczos algorithms for solving matrix eigenvalue problems
type: Item
instance of: scholarly article
title: Arnoldi versus nonsymmetric Lanczos algorithms for solving matrix eigenvalue problems
zbMATH Open document ID: 0861.65032
DOI: 10.1007/BF01731928
author: Jane K. Cullum
published in: BIT
publication date: 1997-04-29T00:00:00Z
review text: A comparison is made between the Arnoldi and the nonsymmetric Lanczos process for computing eigenvalues of nonsymmetric matrices. It is shown that the two processes are similar in the sense that any type of convergence behaviour obtained in exact arithmetic by the nonsymmetric Lanczos process may also be obtained by the Arnoldi procedure applied to another, but related, matrix and a different starting vector. Naturally, one is more interested in a comparison when both algorithms are applied to the same matrix and starting vector. From this, numerical experiments were designed and carried out. The results indicate that the nonsymmetric Lanczos procedure might be less sensitive to deviations from normality, but that the Arnoldi process might converge faster for nearly normal matrices.
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 934132
zbMATH Keywords: matrix eigenvalue problems
zbMATH Keywords: Arnoldi methods
zbMATH Keywords: Lanczo methods
zbMATH Keywords: numerical examples
zbMATH Keywords: eigenvalues
zbMATH Keywords: nonsymmetric matrices
zbMATH Keywords: convergence
zbMATH Keywords: nearly normal matrices
reviewed by: Hermann G. Matthies
describes a project that uses: eigs
describes a project that uses: IRAM
describes a project that uses: Matlab
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01731928
OpenAlex ID: W2053245975
description: scientific article; zbMATH DE number 934132