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dc.contributor.authorLiesen, Jörg
dc.description.abstractWe show that the adjoint of a matrix with respect to a given inner product is a rational function in the matrix, if and only if the matrix is normal with respect to the inner product. We consider such matrices and analyze the McMillan degrees of the rational functions such that the matrix adjoint is a rational function in the matrix. We introduce the McMillan degree of the matrix as the smallest among these degrees, characterize this degree in terms of the number and distribution of the matrix eigenvalues, and compare the McMillan degree with the normal degree of the matrix, which is defined as the smallest degree of a polynomial for which the matrix adjoint is a polynomial in the matrix. We show that unless the matrix eigenvalues lie on a single circle in the complex plane, the ratio of McMillan degree and normal degree of the matrix is bounded by a small constant that depends neither on the number nor on the distribution of the matrix eigenvalues. Our analysis is motivated by applications in the area of short recurrence Krylov subspace methods.en
dc.subject.ddc510 Mathematiken
dc.subject.othernormal matricesen
dc.subject.otherrepresentation of matrix adjointsen
dc.subject.otherrational interpolationen
dc.subject.otherKrylov subspace methodsen
dc.subject.othershort recurrencesen
dc.titleWhen is the adjoint of a matrix a low degree rational function in the matrix?en
dc.typeResearch Paperen
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2006, 23en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften » Inst. Mathematikde
tub.subject.msc200015A21 Canonical forms, reductions, classificationen
tub.subject.msc200030C15 Zeros of polynomials, rational functions, and other analytic functionsen
tub.subject.msc200065F10 Iterative methods for linear systemsen
Appears in Collections:Technische Universität Berlin » Publications

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