Publication:
Locating a nearest matrix with an eigenvalue of prespecified algebraic multiplicity

dc.contributor.coauthorN/A
dc.contributor.departmentDepartment of Mathematics
dc.contributor.kuauthorMengi, Emre
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.date.accessioned2024-11-10T00:00:27Z
dc.date.issued2011
dc.description.abstractThe Wilkinson distance of a matrix A is the two-norm of the smallest perturbation E so that A + E has a multiple eigenvalue. Malyshev derived a singular value optimization characterization for the Wilkinson distance. In this work we generalize the definition of the Wilkinson distance as the two-norm of the smallest perturbation so that the perturbed matrix has an eigenvalue of prespecified algebraic multiplicity. We provide a singular value characterization for this generalized Wilkinson distance. Then we outline a numerical technique to solve the derived singular value optimization problems. In particular the numerical technique is applicable to Malyshev's formula to compute the Wilkinson distance as well as to retrieve a nearest matrix with a multiple eigenvalue.
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.issue1
dc.description.openaccessNO
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuTÜBİTAK
dc.description.sponsorshipNational Science Foundation [DMS-0715146, DMS-0821816]
dc.description.sponsorshipTUBITAK(the scientific and technological research council of Turkey) [109T660] The computing resources for this work were supplied through the National Science Foundation Grants DMS-0715146 and DMS-0821816. This work was also supported in part by the TUBITAK(the scientific and technological research council of Turkey) Grant 109T660. Most of this work was completed when the author was holding a S.E.W. assistant professorship in the department of mathematics at the University of California, San Diego.
dc.description.volume118
dc.identifier.doi10.1007/s00211-010-0326-3
dc.identifier.issn0029-599X
dc.identifier.quartileQ1
dc.identifier.scopus2-s2.0-79954631165
dc.identifier.urihttps://doi.org/10.1007/s00211-010-0326-3
dc.identifier.urihttps://hdl.handle.net/20.500.14288/15798
dc.identifier.wos289442100005
dc.keywordsIll-conditioned eigenproblem
dc.keywordsSpectral decomposition
dc.keywordsPerturbation-theory
dc.keywordsEigendecompositions
dc.keywordsOptimization
dc.keywordsComputation
dc.keywordsConstant
dc.keywordsFormula
dc.keywordsSet
dc.language.isoeng
dc.publisherSpringer
dc.relation.ispartofNumerische Mathematik
dc.subjectMathematics
dc.subjectApplied mathematics
dc.titleLocating a nearest matrix with an eigenvalue of prespecified algebraic multiplicity
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorMengi, Emre
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Mathematics
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relation.isOrgUnitOfPublication.latestForDiscovery2159b841-6c2d-4f54-b1d4-b6ba86edfdbe
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