A numerically strongly stable method for computing the Hamiltonian Schur form

dc.contributor.authorChu, Delin
dc.contributor.authorLiu, Xinmin
dc.contributor.authorMehrmann, Volker
dc.date.accessioned2021-12-17T10:06:00Z
dc.date.available2021-12-17T10:06:00Z
dc.date.issued2004-10-04
dc.description.abstractIn this paper we solve a long-standing open problem in numerical analysis called 'Van Loan's Curse'. We derive a new numerical method for computing the Hamiltonian Schur form of a Hamiltonian matrix that has no purely imaginary eigenvalues. The proposed method is numerically strongly backward stable, i.e., it computes the exact Hamiltonian Schur form of a nearby Hamiltonian matrix, and it is of complexity O(n^3) and thus Van Loan's curse is lifted. We demonstrate the quality of the new method by showing its performance for the benchmark collection of continuous-time algebraic Riccati equations.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15530
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14303
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.otherHamiltonian matrixen
dc.subject.otherskew-Hamiltonian matrixen
dc.subject.otherreal Hamiltonian Schur formen
dc.subject.otherreal skew-Hamiltonian Schur formen
dc.subject.othersymplectic URV-decompositionen
dc.subject.otherstable invariant subspaceen
dc.titleA numerically strongly stable method for computing the Hamiltonian Schur formen
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.issuenumber2004, 24en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200065F15 Eigenvalues, eigenvectorsen
tub.subject.msc200093B36 H∞-controlen
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