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.
Author: | Ralph Byers, Volker Mehrmann, Hongguo Xu |
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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 |