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dc.contributor.authorKonstantinov, Mihail
dc.contributor.authorMehrmann, Volker
dc.contributor.authorPetkov, Petko
dc.contributor.authorGu, Dawei
dc.description.abstractA general framework is presented for the local and non-local perturbation analysis of general real and complex matrix equations in the form $F(P,X) = 0$, where $F$ is a continuous, matrix valued function, $P$ is a collection of matrix parameters and $X$ is the unknown matrix. The local perturbation analysis produces condition numbers and improved first order homogeneous perturbation bounds for the norm $\|\de X\|$ or the absolute value $|\de X|$ of $\de X$. The non-local perturbation analysis is based on the method of Lyapunov majorants and fixed point principles. % for the operator $\pi(p,\cdot)$. It gives rigorous non-local perturbation bounds as well as conditions for solvability of the perturbed equation. The general framework can be applied to various matrix perturbation problems in science and engineering. We illustrate the procedure with several simple examples. Furhermore, as a model problem for the new framework we derive a new perturbation theory for continuous-time algebraic matrix Riccati equations in descriptor form, $Q + A^HXE + E^HXA - E^HXSXE = 0$. The associated equation $Q + A^HXE + E^HX^HA - E^HX^HSXE = 0$ is also briefly considered.en
dc.subject.ddc510 Mathematiken
dc.subject.otherperturbation analysisen
dc.subject.othergeneral matrix equationsen
dc.subject.otherdescriptor Riccati equationsen
dc.titleA general framework for the perturbation theory of matrix equationsen
dc.typeResearch Paperen
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2002, 760en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften » Inst. Mathematikde
tub.subject.msc200015A24 Matrix equations and identitiesen
tub.subject.msc200093C73 Perturbationsen
Appears in Collections:Technische Universität Berlin » Publications

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