Computing the singular value decompostion of a product of two matrices
SIAM Journal on Scientific and Statistical Computing
The calculation of Lyapunov spectra
Physica D
An accurate product SVD algorithm
Signal Processing - Theme issue on singular value decomposition
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
On Smooth Decompositions of Matrices
SIAM Journal on Matrix Analysis and Applications
Lyapunov Spectral Intervals: Theory and Computation
SIAM Journal on Numerical Analysis
Smooth SVD on the Lorentz group with application to computation of Lyapunov exponents
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
Computing Sacker-Sell spectra in Discrete Time Dynamical Systems
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
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In this work 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 [L. Dieci, C. Elia, The singular value decomposition to approximate spectra of dynamical systems. Theoretical aspects, J. Diff. Equat., in press].