Year: 2020
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Peiris, V., Sharon, N., Ugon, N. Sukhorukova J.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3007314130