Methods have previously been developed for the approximation of Lyapunov
functions using radial basis functions. However these methods assume that the
evolution equations are known. We consider the problem of approximating a given
Lyapunov function using radial basis functions where the evolution equations
are not known, but we instead have sampled data which is contaminated with
noise. We propose an algorithm in which we first approximate the underlying
vector field, and use this approximation to then approximate the Lyapunov
function. Our approach combines elements of machine learning/statistical
learning theory with the existing theory of Lyapunov function approximation.
Error estimates are provided for our algorithm.