Approximation of spectral intervals and associated leading directions for linear differential-algebraic systems via smooth singular value decompositions

Please always quote using this URN:urn:nbn:de:0296-matheon-7028
  • This paper is devoted to the numerical approximation of Lyapunov and Sacker-Sell spectral intervals for linear differential-algebraic equations (DAEs). The spectral analysis for DAEs is improved and the concepts of leading directions and solution subspaces associated with spectral intervals are extended to DAEs. Numerical methods based on smooth singular value decompositions are introduced for computing all or only some spectral intervals and their associated leading directions. The numerical algorithms as well as implementation issues are discussed in detail and numerical examples are presented to illustrate the theoretical results.

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Metadaten
Author:Vu Hoang Linh, Volker Mehrmann
URN:urn:nbn:de:0296-matheon-7028
Referee:Peter Deuflhard
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2010/08/24
Release Date:2010/07/08
Tag:
Institute:Technische Universität Berlin
MSC-Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Dxx Stability theory [See also 37C75, 93Dxx] / 34D08 Characteristic and Lyapunov exponents
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Dxx Stability theory [See also 37C75, 93Dxx] / 34D09 Dichotomy, trichotomy
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L07 Numerical investigation of stability of solutions
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L80 Methods for differential-algebraic equations
Preprint Number:711
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