<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> approximation capability of RBF neural networks期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Lp approximation capability of RBF neural networks

Authors:	Dong Nan Wei Wu Jin Ling Long Yu Mei Ma Lin Jun Sun

Affiliation:	(1) Applied Mathematics Department, Dalian University of Technology, Dalian, 116024, P. R. China;(2) Department of Computer, Dalian Nationalities University, Dalian, 116600, P. R. China

Abstract:	L ^p approximation capability of radial basis function (RBF) neural networks is investigated. If g: R ₊¹ → R ¹ and $g(parallel xparallel _{R^n } )$ ∈ L _loc^p(R ⁿ) with 1 ≤ p < ∞, then the RBF neural networks with g as the activation function can approximate any given function in L ^p(K) with any accuracy for any compact set K in R ⁿ, if and only if g(x) is not an even polynomial. Partly supported by the National Natural Science Foundation of China (10471017)

Keywords:	neural networks radial basis function L ^p approximation capability
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