Perturbation theory for Hamiltonian matrices and the distance to bounded-realness

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dc.contributor.authorAlam, Rafikul
dc.contributor.authorBora, Shreemayee
dc.contributor.authorKarow, Michael
dc.contributor.authorMehrmann, Volker
dc.contributor.authorMoro, Julio
dc.date.accessioned2017-12-14T15:42:19Z
dc.date.available2017-12-14T15:42:19Z
dc.date.issued2011-06-27
dc.description.abstractMotivated by the analysis of passive control systems, we undertake a detailed perturbation analysis of Hamiltonian matrices that have eigenvalues on the imaginary axis. We construct minimal Hamiltonian perturbations that move and coalesce eigenvalues of opposite sign characteristic to form multiple eigenvalues with mixed sign characteristics, which are then moved from the imaginary axis to specific locations in the complex plane by small Hamiltonian perturbations. We also present a numerical method to compute upper bounds for the minimal perturbations that move all eigenvalues of a given Hamiltonian matrix outside a vertical strip along the imaginary axis.en
dc.identifier.eissn1095-7162
dc.identifier.issn0895-4798
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/7277
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-6550
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc519 Wahrscheinlichkeiten, angewandte Mathematikde
dc.subject.ddc518 Numerische Analysisde
dc.subject.otherHamiltonian matrixen
dc.subject.otherHamiltonian eigenvalue problemen
dc.subject.otherstructured mapping problemen
dc.subject.otherdistance to bounded-realnessen
dc.subject.otherperturbation theoryen
dc.subject.otherpassive systemen
dc.subject.otherbounded-realnessen
dc.subject.otherpurely imaginary eigenvaluesen
dc.subject.othersign characteristicen
dc.subject.otherHamiltonian pseudospectraen
dc.titlePerturbation theory for Hamiltonian matrices and the distance to bounded-realnessen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.doi10.1137/10079464Xen
dcterms.bibliographicCitation.issue2en
dcterms.bibliographicCitation.journaltitleSIAM Journal on Matrix Analysis and Applicationsen
dcterms.bibliographicCitation.originalpublishernameSociety for Industrial and Applied Mathematicsen
dcterms.bibliographicCitation.originalpublisherplacePhiladelphia, Pa.en
dcterms.bibliographicCitation.pageend514en
dcterms.bibliographicCitation.pagestart484en
dcterms.bibliographicCitation.volume32en
tub.accessrights.dnbdomainen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::FG Numerische Lineare Algebrade
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.groupFG Numerische Lineare Algebrade
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen

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