  A rational approximation by a ratio of polynomial functions is a flexible
alternative to polynomial approximation. In particular, rational functions
exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where
polynomial approximations are not efficient. We prove that the optimisation
problems appearing in the best uniform rational approximation are quasiconvex,
and show how to use this fact for calculating the best approximation in a fast
and efficient method. The paper presents a theoretical study of the arising
optimisation problems and provides results of several numerical experiments. In
all our computations, the algorithms terminated at optimal solutions. We apply
our approximation as a preprocess step to deep learning classifiers and
demonstrate that the classification accuracy is significantly improved compared
to the classification of the raw signals.
