A method for separating nearly multiple eigenvalues for Hermitian matrix
type: Item
instance of: scholarly article
title: A method for separating nearly multiple eigenvalues for Hermitian matrix
zbMATH Open document ID: 1112.65032
published in: Journal of Computational and Applied Mathematics
publication date: 2007-02-02T00:00:00Z
review text: The following problem is discussed: Given a symmetric matrix and assume that by one of the methods of verified computation a small interval has been determined which encloses \(k\) of its eigenvalues. Verify that they are not a k-fold eigenvalue. An algorithm using verified computation, e.g. using INTLAB, is given, which can decide this question. Two examples with \(k=2\) (the infamous Wilkinson matrix) and \(k=3\) illustrate the method.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65G20
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 5121442
zbMATH Keywords: multiple eigenvalue
zbMATH Keywords: symmetric matrix
zbMATH Keywords: verified computation
zbMATH Keywords: numerical examples
zbMATH Keywords: eigenvalue enclosure
zbMATH Keywords: algorithm
zbMATH Keywords: Wilkinson matrix
author: Kenji Toyonaga
reviewed by: Ludwig Elsner
describes a project that uses: INTLAB
MaRDI profile type: Publication
full work available at URL: j.cam.2005.08.040
OpenAlex ID: W1995356329
cites work: Q4949347
cites work: Computational error bounds for multiple or nearly multiple eigenvalues
cites work: Q5674306
cites work: A simple method for error bounds of eigenvalues of symmetric matrices
DOI: 10.1016/J.CAM.2005.08.040
description: scientific article; zbMATH DE number 5121442