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Indexed by:期刊论文

Date of Publication:2008-09-01

Journal:ACTA MATHEMATICA SINICA-ENGLISH SERIES

Included Journals:ISTIC、CSCD、SCIE、Scopus

Volume:24

Issue:9

Page Number:1533-1540

ISSN No.:1439-8516

Key Words:neural networks; radial basis function; L(p) approximation capability

Abstract:L(p) approximation capability of radial basis Function (RBF) neural networks is investigated. If g : R(+)(1) -> R(1) and g(parallel to x parallel to(n)(R)) epsilon L(loc)(p)(R(n)) with 1 <= p <= infinity, then the RBF neural networks with g as the activation function can approximate any given function in LP(K) with any accuracy for any compact set K in R(n), if and only if g(x) is not an even polynomial.