Best Neural Network Approximation by using Bernstein Polynomials with GRNN Learning Application

Abstract

Bernstein polynomials are one of the fi rst and main tools for function approximation. On the other hand, neural networks have many useful applications in approximation and other fi elds as well. In this paper, we study how we bene fi t from properties of Bernstein polynomials to de fi ne a new version of neural networks, that can be fi t approxi-mating functions in terms of modulus of continuity. Numerically, we use neural networks to approximate some types of continuous functions. For that purpose, we use GRNN algorithm to approximate functions uniformly by using Matlab, giving some examples that con fi rm good rate approximation.