L~p(K) Approximation Problems in System Identification with RBF Neural Networks
Long Jin · Journal of Mathematical Research and Exposition · 2009
Lp approximation problems in system identification with RBF neural networks are investigated.It is proved that by superpositions of some functions of one variable in Lploc(R),one can approximate continuous functionals defined on a compact subset of Lp(K) and continuous operators from a compact subset of Lp1(K1) to a compact subset of Lp2(K2).These results show that if its activation function is in Llpoc(R) and is not an even polynomial,then this RBF neural networks can approximate the above systems with any accuracy.