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dc.contributor.authorMehrmann, Volker
dc.contributor.authorWatkins, David
dc.description.abstractWe discuss the numerical solution of eigenvalue problems for matrix polynomials, where the coefficient matrices are alternating symmetric and skew symmetric or Hamiltonian and skew Hamiltonian. We discuss several applications that lead to such structures. Matrix polynomials of this type have a symmetry in the spectrum that is the same as that of Hamiltonian matrices or skew-Hamiltonian/Hamiltonian pencils. The numerical methods that we derive are designed to preserve this eigenvalue symmetry. We also discuss linearization techniques that transform the polynomial into a skew-Hamiltonian/Hamiltonian linear eigenvalue problem with a specific substructure. For this linear eigenvalue problem we discuss special factorizations that are useful in shift-and-invert Krylov subspace methods for the solution of the eigenvalue problem. We present a numerical example that demonstrates the effectiveness of our approach.en
dc.subject.ddc510 Mathematiken
dc.subject.othermatrix polynomialen
dc.subject.otherHamiltonian matrixen
dc.subject.otherskew-Hamiltonian matrixen
dc.subject.otherskew-Hamiltonian/Hamiltonian pencilen
dc.subject.othermatrix factorizationsen
dc.titlePolynomial Eigenvalue Problems with Hamiltonian Structureen
dc.typeResearch Paperen
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2002, 724en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften » Inst. Mathematikde
tub.subject.msc200065F15 Eigenvalues, eigenvectorsen
tub.subject.msc200015A18 Eigenvalues, singular values, and eigenvectorsen
Appears in Collections:Technische Universität Berlin » Publications

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