L~p Approximation Capability of RBF Neural Networks

L~p Approximation Capability of RBF Neural Networks

<正> Lp approximation capability of radial basis function（RBF）neural networks is investigated.Ifg:R+1→R1 and g(‖x‖Rn)∈ L（loc）p（Rn）with 1≤p<∞,then the RBF neural networks with g as theactivation function can approximate any given function in Lp（K）with any accuracy for any compacts...

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Veröffentlicht in:Acta mathematica Sinica. English series 2008-09, Vol.24 (9), p.1533-1540
Hauptverfasser: Nan, Dong, Wu, Wei, Long, Jin Ling, Ma, Yu Mei, Sun, Lin Jun
Format: Artikel
Sprache:eng
Schlagworte:
approximation
basis
capability
function
L~p
networks
neural
radial
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Zusammenfassung:<正> Lp approximation capability of radial basis function（RBF）neural networks is investigated.Ifg:R+1→R1 and g(‖x‖Rn)∈ L（loc）p（Rn）with 1≤p<∞,then the RBF neural networks with g as theactivation function can approximate any given function in Lp（K）with any accuracy for any compactset K in Rn,if and only if g（x）is not an even polynomial.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-008-6423-x