Publication:
Matrix polynomials with specified eigenvalues

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dc.contributor.coauthorKarow, Michael
dc.contributor.departmentDepartment of Mathematics
dc.contributor.kuauthorMengi, Emre
dc.contributor.kuprofileFaculty Member
dc.contributor.otherDepartment of Mathematics
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.contributor.yokid113760
dc.date.accessioned2024-11-09T23:39:09Z
dc.date.issued2015
dc.description.abstractThis work concerns the distance in the 2-norm from a given matrix polynomial to a nearest polynomial with a specified number of its eigenvalues at specified locations in the complex plane. Initially, we consider perturbations of the constant coefficient matrix only. A singular value optimization characterization is derived for the associated distance. We also consider the distance in the general setting, when all of the coefficient matrices are perturbed. In this general setting, we obtain a lower bound in terms of another singular value optimization problem. The singular value optimization problems derived facilitate the numerical computation of the distances.
dc.description.indexedbyWoS
dc.description.indexedbyScopus
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsorshipEuropean Commission grant [PIRG-GA-268355]
dc.description.sponsorshipTUBITAK(the scientific and technological research council of Turkey) [109T660]
dc.description.sponsorshipBAGEP program of Turkish Academy of Science We are grateful to Daniel Kressner for reading an initial version and providing helpful suggestions. His suggestions directed us to the simplified divided difference formulas in Section 3.5. We also thank Froilan Dopico, Michael Overton, Francoise Tisseur and an anonymous referee for their valuable feedback. The work of Emre Mengi was supported in part by the European Commission grant PIRG-GA-268355, the TUBITAK(the scientific and technological research council of Turkey) carrier grant 109T660, and by the BAGEP program of Turkish Academy of Science.
dc.description.volume466
dc.identifier.doi10.1016/j.laa.2014.10.010
dc.identifier.eissn1873-1856
dc.identifier.issn0024-3795
dc.identifier.quartileQ2
dc.identifier.scopus2-s2.0-84909983076
dc.identifier.urihttp://dx.doi.org/10.1016/j.laa.2014.10.010
dc.identifier.urihttps://hdl.handle.net/20.500.14288/13068
dc.identifier.wos347024400029
dc.keywordsMatrix polynomial
dc.keywordsLinearization
dc.keywordsSingular values
dc.keywordsSylvester equation
dc.keywordsEigenvalue perturbation theory
dc.keywordsMultiple-eigenvalues
dc.keywordsCritical-points
dc.keywordsPseudospectra
dc.keywordsDistance
dc.keywordsFormula
dc.languageEnglish
dc.publisherElsevier Science Inc
dc.sourceLinear Algebra and Its Applications
dc.subjectMathematics
dc.subjectApplied mathematics
dc.titleMatrix polynomials with specified eigenvalues
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.authorid0000-0003-0788-0066
local.contributor.kuauthorMengi, Emre
relation.isOrgUnitOfPublication2159b841-6c2d-4f54-b1d4-b6ba86edfdbe
relation.isOrgUnitOfPublication.latestForDiscovery2159b841-6c2d-4f54-b1d4-b6ba86edfdbe

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