On the convergence of a new Rayleigh quotient method with applications to large eigenproblems
type: Item
instance of: scholarly article
title: On the convergence of a new Rayleigh quotient method with applications to large eigenproblems
zbMATH Open document ID: 0912.65028
author: G. W. Stewart
author: Dianne P. O'Leary
publication date: 1999-02-08T00:00:00Z
full work available at URL: https://eudml.org/doc/119750
full work available at URL: vol.7.1998
review text: A variant of the Rayleigh quotient method is proposed to compute an eigenvalue and corresponding eigenvectors of a matrix. This variant called singular vector Rayleigh quotient method uses the observation that eigenvectors of a matrix with eigenvalue zero are also singular vectors corresponding to zero singular values. If these singular vectors are computed exactly the method is quadratically convergent. But exact singular vectors are not required for convergence. The method may be useful for large eigenvalue problems. The decomposition associated with a simple eigenvalue, the generalized Rayleigh quotients, and the convergence of the algorithm are discussed. Implicitly in the analysis is a relation between the inferior singular vector of the matrix and an eigenvector corresponding to a small eigenvalue.
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 1249444
zbMATH Keywords: singular value decomposition
zbMATH Keywords: eigenvalue
zbMATH Keywords: eigenvectors
zbMATH Keywords: singular vector Rayleigh quotient method
zbMATH Keywords: convergence
zbMATH Keywords: large eigenvalue problems
zbMATH Keywords: algorithm
describes a project that uses: JDQR
describes a project that uses: eigs
MaRDI profile type: Publication
published in: ETNA - Electronic Transactions on Numerical Analysis
description: scientific article; zbMATH DE number 1249444