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SVD algorithms to approximate spectra of dynamical systems. (English) Zbl 1166.65363

Summary: We consider algorithms based on the singular value decomposition (SVD) to approximate Lyapunov and exponential dichotomy spectra of dynamical systems. We review existing contributions, and propose new algorithms of the continuous SVD method. We present implementation details for the continuous SVD method, and illustrate on several examples the behavior of continuous (and also discrete) SVD method. This paper is the companion paper of [the authors, J. Differ. Equations 230, No. 2, 502–531 (2006; Zbl 1139.93014)].

MSC:

65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
15A18 Eigenvalues, singular values, and eigenvectors
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
65L07 Numerical investigation of stability of solutions to ordinary differential equations

Citations:

Zbl 1139.93014

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References:

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