Neural Network of Multivariate Square Rational Bernstein Operators with Positive Integer Parameter

Abstract

This research is defined a new neural network (NN) that depends upon a positive integer parameter using the multivariate square rational Bernstein polynomials. Some theorems for this network are proved, such as the pointwise and the uniform approximation theorems. Firstly, the absolute moment for a function that belongs to Lipschitz space is defined to estimate the order of the NN. Secondly, some numerical applications for this NN are given by taking two test functions. Finally, the numerical results for this network are compared with the classical neural networks (NNs). The results turn out that the new network is better than the classical one.