L^p（K）Approximation Problems in System Identification with RBF Neural Networks  

作　　者：NAN Dong LONG Jin Ling 

机构地区：[1]Applied Mathematics Department, Dalian University of Technology, Liaoning 116024, China

出　　处：《Journal of Mathematical Research and Exposition》2009年第1期124-128,共5页数学研究与评论（英文版）

基　　金：Foundation item： tile National Natural Science Foundation of China （No. 10471017）.

摘　　要：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^ploc（R）, one can approximate continuous functionals defined on a compact subset of L^P（K） and continuous operators from a compact subset of L^p1 （K1） to a compact subset of L^p2 （K2）. These results show that if its activation function is in L^ploc（R） and is not an even polynomial, then this RBF neural networks can approximate the above systems with any accuracy.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^ploc（R）, one can approximate continuous functionals defined on a compact subset of L^P（K） and continuous operators from a compact subset of L^p1 （K1） to a compact subset of L^p2 （K2）. These results show that if its activation function is in L^ploc（R） and is not an even polynomial, then this RBF neural networks can approximate the above systems with any accuracy.

关 键 词：RBF neural networks system identification LP-approximation continuous functionals and operators. 

分 类 号：O174.41[理学—数学]