$L^p(K)$ Approximation Problems in System Identification with RBF Neural Networks
Received:January 03, 2007  Revised:May 26, 2007
Key Word: RBF neural networks   system identification   $L^p$-approximation   continuous functionals and operators.  
Fund ProjectL:the National Natural Science Foundation of China (No.10471017).
Author NameAffiliation
NAN Dong Applied Mathematics Department, Dalian University of Technology, Liaoning 116024, China 
LONG Jin Ling Applied Mathematics Department, Dalian University of Technology, Liaoning 116024, China 
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Abstract:
      $L^p$ approximation problems in system identification with RBF neural networks are investigated. It is proved that by superpositions of some functions of one variable in $L^p_{\rm loc}({\mathbb R})$, one can approximate continuous functionals defined on a compact subset of $L^p(K)$ and continuous operators from a compact subset of $L^{p_1}(K_1)$ to a compact subset of $L^{p_2}(K_2)$. These results show that if its activation function is in $L^p_{\rm loc}({\mathbb R})$ and is not an even polynomial, then this RBF neural networks can approximate the above systems with any accuracy.
Citation:
DOI:10.3770/j.issn:1000-341X.2009.01.016
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