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Staircase forms and trimmed linearizations for structured matrix polynomials

Please always quote using this URN:urn:nbn:de:0296-matheon-3944
  • We discuss the eigenvalue problem for general and structured matrix polynomials which may be singular and may have eigenvalues at infinity. We derive staircase condensed forms that allow deflation of the infinite eigenvalue and singular structure of the matrix polynomial. The remaining reduced order staircase form leads to new types of linearizations which determine the finite eigenvalues and and corresponding eigenvectors. The new linearizations also simplify the construction of structure preserving linearizations.

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Metadaten
Author:Ralph Byers, Volker Mehrmann, Hongguo Xu
URN:urn:nbn:de:0296-matheon-3944
Referee:Carsten Carstensen
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2007/03/07
Release Date:2007/05/25
Tag:
Institute:Technische Universität Berlin
MSC-Classification:15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A21 Canonical forms, reductions, classification
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Axx General theory / 34A30 Linear equations and systems, general
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F15 Eigenvalues, eigenvectors
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L05 Initial value problems
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L80 Methods for differential-algebraic equations
Preprint Number:395
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