On condition numbers of polynomial eigenvalue problems

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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 http://hdl.handle.net/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

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