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.
Author: | Vu Hoang Linh, Volker Mehrmann |
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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 |