An improved grid method for the computation of the pseudospectra of matrix polynomials

Fatouros, S; Psarrakos, P

dc.contributor.author	Fatouros, S	en
dc.contributor.author	Psarrakos, P	en
dc.date.accessioned	2014-03-01T01:29:50Z
dc.date.available	2014-03-01T01:29:50Z
dc.date.issued	2009	en
dc.identifier.issn	0895-7177	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19364
dc.subject	ε-pseudospectrum	en
dc.subject	Eigenvalue	en
dc.subject	Matrix polynomial	en
dc.subject	Perturbation	en
dc.subject.classification	Computer Science, Interdisciplinary Applications	en
dc.subject.classification	Computer Science, Software Engineering	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Control theory	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.subject.other	Matrix algebra	en
dc.subject.other	Polynomials	en
dc.subject.other	Switching systems	en
dc.subject.other	Computational costs	en
dc.subject.other	Eigenvalue	en
dc.subject.other	Eigenvalue problems	en
dc.subject.other	Grid methods	en
dc.subject.other	Illustrative examples	en
dc.subject.other	Lower bounds	en
dc.subject.other	Matrix polynomial	en
dc.subject.other	Matrix polynomials	en
dc.subject.other	Perturbation	en
dc.subject.other	Polynomial eigenvalue problems	en
dc.subject.other	Pseudospectra	en
dc.subject.other	Polynomial approximation	en
dc.title	An improved grid method for the computation of the pseudospectra of matrix polynomials	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.mcm.2008.05.047	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.mcm.2008.05.047	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	Pseudospectra of matrix polynomials have been systematically investigated in recent years, since they provide important insights into the sensitivity of polynomial eigenvalue problems. An accurate approximation of the pseudospectrum of a matrix polynomial P(lambda) by means of the standard grid method is highly demanding computationally. In this paper, we propose an improvement of the grid method, which reduces the computational cost and retains the robustness and the parallelism of the method. In particular, after giving two lower bounds for the distance from a point to the boundary of the pseudospectrum of P(lambda), we present two algorithms for the estimation of the pseudospectrum, using exclusion discs. Furthermore, two illustrative examples and an application of pseudospectra on elliptic (quadratic) eigenvalue problems are given. (C) 2008 Elsevier Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	Mathematical and Computer Modelling	en
dc.identifier.doi	10.1016/j.mcm.2008.05.047	en
dc.identifier.isi	ISI:000260904100007	en
dc.identifier.volume	49	en
dc.identifier.issue	1-2	en
dc.identifier.spage	55	en
dc.identifier.epage	65	en