On the condition numbers of a multiple eigenvalue of a generalized eigenvalue problem
type: Item
instance of: scholarly article
title: On the condition numbers of a multiple eigenvalue of a generalized eigenvalue problem
zbMATH Open document ID: 1252.15012
author: Yuji Nakatsukasa
published in: Numerische Mathematik
publication date: 2012-08-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1008.1201
full work available at URL: multieigRR.pdf
review text: The author deals with the condition numbers of a multiple eigenvalue of a generalized eigenvalue problem. First under Hermitian perturbations of a Hermitian definite pair with a nondefective multiple finite eigenvalue, the author provides the condition numbers of this eigenvalue. After, he provides the condition numbers of a finite multiple eigenvalue of a non Hermitian pair under non Hermitian perturbations. These condition numbers are characterized in terms of the singular values of the outer product of the corresponding left and right eigenvectors. In addition, the author also studies the case of an infinite and/or defective eigenvalue. Numerical examples are also given to illustrate the results of the article.
reviewed by: Ioannis K. Dassios
Mathematics Subject Classification ID: 15A22
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 6065179
zbMATH Keywords: condition numbers
zbMATH Keywords: multiple eigenvalue
zbMATH Keywords: generalized eigenvalue problem
zbMATH Keywords: Hermitian perturbations
zbMATH Keywords: Hermitian definite pair
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
OpenAlex ID: W2051533026
arXiv ID: 1008.1201
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DOI: 10.1007/S00211-011-0440-X
description: scientific article; zbMATH DE number 6065179