Publication: Locating a nearest matrix with an eigenvalue of prespecified algebraic multiplicity
dc.contributor.coauthor | N/A | |
dc.contributor.department | Department of Mathematics | |
dc.contributor.kuauthor | Mengi, Emre | |
dc.contributor.schoolcollegeinstitute | College of Sciences | |
dc.date.accessioned | 2024-11-10T00:00:27Z | |
dc.date.issued | 2011 | |
dc.description.abstract | The 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.indexedby | WOS | |
dc.description.indexedby | Scopus | |
dc.description.issue | 1 | |
dc.description.openaccess | NO | |
dc.description.publisherscope | International | |
dc.description.sponsoredbyTubitakEu | TÜBİTAK | |
dc.description.sponsorship | National Science Foundation [DMS-0715146, DMS-0821816] | |
dc.description.sponsorship | TUBITAK(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.volume | 118 | |
dc.identifier.doi | 10.1007/s00211-010-0326-3 | |
dc.identifier.issn | 0029-599X | |
dc.identifier.quartile | Q1 | |
dc.identifier.scopus | 2-s2.0-79954631165 | |
dc.identifier.uri | https://doi.org/10.1007/s00211-010-0326-3 | |
dc.identifier.uri | https://hdl.handle.net/20.500.14288/15798 | |
dc.identifier.wos | 289442100005 | |
dc.keywords | Ill-conditioned eigenproblem | |
dc.keywords | Spectral decomposition | |
dc.keywords | Perturbation-theory | |
dc.keywords | Eigendecompositions | |
dc.keywords | Optimization | |
dc.keywords | Computation | |
dc.keywords | Constant | |
dc.keywords | Formula | |
dc.keywords | Set | |
dc.language.iso | eng | |
dc.publisher | Springer | |
dc.relation.ispartof | Numerische Mathematik | |
dc.subject | Mathematics | |
dc.subject | Applied mathematics | |
dc.title | Locating a nearest matrix with an eigenvalue of prespecified algebraic multiplicity | |
dc.type | Journal Article | |
dspace.entity.type | Publication | |
local.contributor.kuauthor | Mengi, Emre | |
local.publication.orgunit1 | College of Sciences | |
local.publication.orgunit2 | Department of Mathematics | |
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