Original scientific paper

The construction and approximation of neural networks operators with Gaussian activation function

Zhixiang Chen ; Department of Mathematics, Shaoxing University, Shaoxing, Zhejiang Province, P.R. China
Feilong Cao ; Department of Mathematics, China Jiliang University, Hangzhou, Zhejiang Province, P.R. China

Abstract

This paper studies the construction and approximation of neural network operators with a centered bell-shaped Gaussian activation function. Using a univariate Gaussian function a class of Cardaliaguet-Euvrard type network operators is constructed to approximate the continuous function, and the Jackson type theorems of the approximation and some discussions about the convergence are given. Furthermore, to approximate the multivariate function, a class of bivariate Cardaliaguet-Euvrard type network operators is
introduced, and the corresponding estimates of the approximation rate are deduced.

Keywords

neural network; Gaussian function; approximation; modulus of continuity

Hrčak ID:

101437

URI

https://hrcak.srce.hr/101437

Publication date:

10.5.2013.

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