Distance bounds for prescribed multiple eigenvalues of matrix polynomials

Psarrakos, PJ

dc.contributor.author	Psarrakos, PJ	en
dc.date.accessioned	2014-03-01T02:08:41Z
dc.date.available	2014-03-01T02:08:41Z
dc.date.issued	2012	en
dc.identifier.issn	00243795	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29702
dc.subject	Algebraic multiplicity	en
dc.subject	Eigenvalue	en
dc.subject	Index of annihilation	en
dc.subject	Matrix polynomial	en
dc.subject	Perturbation	en
dc.subject	Singular value	en
dc.subject	Singular vector	en
dc.subject.other	Algebraic multiplicity	en
dc.subject.other	Eigen-value	en
dc.subject.other	Index of annihilation	en
dc.subject.other	Matrix polynomials	en
dc.subject.other	Perturbation	en
dc.subject.other	Singular values	en
dc.subject.other	Singular vectors	en
dc.subject.other	Algebra	en
dc.subject.other	Matrix algebra	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.title	Distance bounds for prescribed multiple eigenvalues of matrix polynomials	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.laa.2012.01.003	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.laa.2012.01.003	en
heal.publicationDate	2012	en
heal.abstract	In this paper,motivated by a problem posed byWilkinson, we study the coefficient perturbations of a (square) matrix polynomial to a matrix polynomial that has a prescribed eigenvalue of specified algebraic multiplicity and index of annihilation. For an n × n matrix polynomial P(λ) and a given scalarμ ∈ ℂ,we introduce two weighted spectral norm distances, εr(μ) and εr,k(μ), from P(λ) to the n × n matrix polynomials that have μ as an eigenvalue of algebraicmultiplicity at least r and to those that haveμas an eigenvalue of algebraicmultiplicity at least r and maximum Jordan chain length (exactly) k, respectively. Then we obtain a lower bound for εr,k(μ), and derive an upper bound for εr(μ) by constructing an associated perturbation of P(λ). © 2012 Elsevier Inc. All rights reserved.	en
heal.journalName	Linear Algebra and Its Applications	en
dc.identifier.doi	10.1016/j.laa.2012.01.003	en
dc.identifier.volume	436	en
dc.identifier.issue	11	en
dc.identifier.spage	4107	en
dc.identifier.epage	4119	en