On condition numbers of polynomial eigenvalue problems

Papathanasiou, N; Psarrakos, P

dc.contributor.author	Papathanasiou, N	en
dc.contributor.author	Psarrakos, P	en
dc.date.accessioned	2014-03-01T01:34:00Z
dc.date.available	2014-03-01T01:34:00Z
dc.date.issued	2010	en
dc.identifier.issn	0096-3003	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20640
dc.subject	Condition number	en
dc.subject	Eigenvalue	en
dc.subject	Matrix polynomial	en
dc.subject	Perturbation	en
dc.subject	Pseudospectrum	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Condition numbers	en
dc.subject.other	Eigen-value	en
dc.subject.other	Eigenvalue problem	en
dc.subject.other	Eigenvalues	en
dc.subject.other	Eigenvectors	en
dc.subject.other	Euclidean norm	en
dc.subject.other	Ill-conditioned	en
dc.subject.other	Matrix perturbation theory	en
dc.subject.other	Matrix polynomials	en
dc.subject.other	Perturbation bounds	en
dc.subject.other	Polynomial eigenvalue problems	en
dc.subject.other	Pseudospectral	en
dc.subject.other	Pseudospectrum	en
dc.subject.other	Upper Bound	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.subject.other	Number theory	en
dc.subject.other	Perturbation techniques	en
dc.subject.other	Polynomials	en
dc.subject.other	Switching systems	en
dc.subject.other	Matrix algebra	en
dc.title	On condition numbers of polynomial eigenvalue problems	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.amc.2010.02.011	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.amc.2010.02.011	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	In this paper, we investigate condition numbers of eigenvalue problems of matrix polynomials with nonsingular leading coefficients, generalizing classical results of matrix perturbation theory. We provide a relation between the condition numbers of eigenvalues and the pseudospectral growth rate. We obtain that if a simple eigenvalue of a matrix polynomial is ill-conditioned in some respects, then it is close to be multiple, and we construct an upper bound for this distance (measured in the euclidean norm). We also derive a new expression for the condition number of a simple eigenvalue, which does not involve eigenvectors. Moreover, an Elsner-like perturbation bound for matrix polynomials is presented. (C) 2010 Elsevier Inc. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE INC	en
heal.journalName	Applied Mathematics and Computation	en
dc.identifier.doi	10.1016/j.amc.2010.02.011	en
dc.identifier.isi	ISI:000276105200017	en
dc.identifier.volume	216	en
dc.identifier.issue	4	en
dc.identifier.spage	1194	en
dc.identifier.epage	1205	en