On the nearest singular matrix pencil

dc.contributor.authorGuglielmi, Nicola
dc.contributor.authorLubich, Christian
dc.contributor.authorMehrmann, Volker
dc.date.accessioned2021-12-17T10:14:21Z
dc.date.available2021-12-17T10:14:21Z
dc.date.issued2016-06-01
dc.description.abstractGiven a regular matrix pencil A + μE, we consider the problem of determining the nearest singular matrix pencil with respect to the Frobenius norm. We present new approaches based on the solution of matrix differential equations for determining the nearest singular pencil A + ΔA + μ(E + ΔE), one approach for general singular pencils and another one such that A+ ΔA and E + ΔE have a common left/right null vector. For the latter case the nearest singular pencil is shown to differ from the original pencil by rank-one matrices ΔA and ΔE. In both cases we consider also the situation where only A is perturbed. The nearest singular pencil is approached by a two-level iteration, where a gradient flow is driven to a stationary point in the inner iteration and the outer level uses a fast iteration for the distance parameter. This approach extends also to structured matrices A and E.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15873
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14646
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.otherregular matrix pencilen
dc.subject.othersingular matrix pencilen
dc.subject.otherdifferential-algebraic equationen
dc.subject.otherlow-rank perturbationen
dc.subject.othermatrix differential equationen
dc.titleOn the nearest singular matrix pencilen
dc.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2016, 12en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200015A18 Eigenvalues, singular values, and eigenvectorsen
tub.subject.msc200065K05 Mathematical programmingen

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