Spectral Perturbation & Optimization of Matrix Pencils

von

Gernandt, Hannes

BuchKartoniert, Paperback

132 Seiten

Englisch

readbox publishingerschienen am23.09.2021

In this thesis we study the eigenvalues of linear matrix pencils and their behavior under perturbations of the pencil coefficients.In particular we address (i) Possibility of eigenvalue assignment under structured rank-one perturbations; (ii) Distance to nearest pencils with a prescribed set of eigenvalues in norm and gap distance; (iii) Computing nearest matrix pencils with prescribed eigenvalues using structured perturbations.In (i) and (ii) we exploit the connection between matrix pencils and certain subspaces via their Weyr characteristics.This provides a way of lifting perturbation measures for subspaces such as the gap distance to the set of matrix pencils.In (iii) one has to solve a large scale non-convex optimization problem which appears e.g. in optimal redesign of integrated circuits.We show how feasible solutions close to the optimal value can be computed.Finally, this is used to improve the bandwidth of two circuits (two-stage CMOS & miA741).mehr

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KlappentextIn this thesis we study the eigenvalues of linear matrix pencils and their behavior under perturbations of the pencil coefficients.In particular we address (i) Possibility of eigenvalue assignment under structured rank-one perturbations; (ii) Distance to nearest pencils with a prescribed set of eigenvalues in norm and gap distance; (iii) Computing nearest matrix pencils with prescribed eigenvalues using structured perturbations.In (i) and (ii) we exploit the connection between matrix pencils and certain subspaces via their Weyr characteristics.This provides a way of lifting perturbation measures for subspaces such as the gap distance to the set of matrix pencils.In (iii) one has to solve a large scale non-convex optimization problem which appears e.g. in optimal redesign of integrated circuits.We show how feasible solutions close to the optimal value can be computed.Finally, this is used to improve the bandwidth of two circuits (two-stage CMOS & miA741).

Details

ISBN/GTIN978-3-86360-246-8

ProduktartBuch

EinbandartKartoniert, Paperback

Verlag

readbox publishing

Erscheinungsjahr2021

Erscheinungsdatum23.09.2021

Seiten132 Seiten

SpracheEnglisch

Gewicht238 g

Illustrationen17 Farbabb.