L^p Approximation Capability of RBF Neural Networks  

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

机构地区：[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

出　　处：《Acta Mathematica Sinica,English Series》2008年第9期1533-1540,共8页数学学报（英文版）

基　　金：the National Natural Science Foundation of China (10471017)

摘　　要：L p approximation capability of radial basis function (RBF) neural networks is investigated. If g: R +1 → R 1 and $g(\parallel x\parallel _{R^n } )$g(\parallel x\parallel _{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.L p approximation capability of radial basis function (RBF) neural networks is investigated. If g: R +1 → R 1 and $g(\parallel x\parallel _{R^n } )$g(\parallel x\parallel _{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.

关 键 词：neural networks radial basis function L p approximation capability 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]