The Rate of Approximation of Gaussian Radial Basis Neural Networks in Continuous Function Space  

作　　者：Ting Fan XIE Fei Long CAO 

机构地区：[1]Institute of Metrology and Computational Science,China Jiliang University

出　　处：《Acta Mathematica Sinica,English Series》2013年第2期295-302,共8页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.61101240and61272023);the Zhejiang Provincial Natural Science Foundation of China(Grant No.Y6110117)

摘　　要：There have been many studies on the dense theorem of approximation by radial basis feedforword neural networks, and some approximation problems by Gaussian radial basis feedforward neural networks （GRBFNs） in some special function space have also been investigated. This paper considers the approximation by the GRBFNs in continuous function space. It is proved that the rate of approximation by GRNFNs with nd neurons to any continuous function f defined on a compact subset K R^d can be controlled by w（f, n^-1/2）, where w（f, t） is the modulus of continuity of the function f.There have been many studies on the dense theorem of approximation by radial basis feedforword neural networks, and some approximation problems by Gaussian radial basis feedforward neural networks （GRBFNs） in some special function space have also been investigated. This paper considers the approximation by the GRBFNs in continuous function space. It is proved that the rate of approximation by GRNFNs with nd neurons to any continuous function f defined on a compact subset K R^d can be controlled by w（f, n^-1/2）, where w（f, t） is the modulus of continuity of the function f.

关 键 词：Gaussian radial basis feedforward neural networks APPROXIMATION rate of convergence modulus of continuity 

分 类 号：O174[理学—数学]