  In this paper we make a detailed numerical comparison between three
algorithms for the computation of the full Lyapunov spectrum as well as the
associated eigen-vectors of general dynamical systems. They are : (a) the
standard method, (b) a differential formaulation of the standard method, and
(c) a new algorithm which does not require rescaling and reorthogonolization.
We also bring out the relations among these methods. oreover, we give a
simplified formulation of the new algorithm when the dimensionality of the
system is 4. We find that there is reasonable agreement among the Lyapunov
spectra obtained using the three algorithms in most cases. However the standard
method seems to be the most efficient followed by the new method and the
differential version of the standard method (in that order), as far as the CPU
time for the computation of the Lyapunov spectra is concerned. The new method
is hardly suitable for finding the eigenvectors, whereas the other procedures
give nearly identical numerical results.
