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
Publication date:
10.5.2013.
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