SVD algorithms to approximate spectra of dynamical systems

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].