子波网络的近似能力分析

Engineering Analysis of Approximation with Wavelet Networks

选取单隐层子波网络为研究对象，并且允许隐层上的节．点数可以足够多，通过对其构成机理的分析，得出一个有关这种网络对非线性映射逼近能力的定理，从数学上给予了严格的证明，并进行了仿真计算，仿真结果表明。

Wavelet networks[2] is useful in our design of information processing system of air-to air missile. In order to be fully confident of correct approximation (correct apporximation means arbitrary target information can always be accurately transmitted and ultilized ), a mathematical proof of the correctness of approximation when wavelet networks is properly applied is offered in this paper.The wavelet networks considered in this paper has only single hidden layer but infinite neurons. That means, in eq. (2), N is any large number and mathematically it can approach Infinity. We prove a theorem that states that g (x )I S are dense in L2 (Rn). That is to say,wavelet networks given by g (x ) can approximate any arbitrary fUnction in L2(Rn) accurately.Two simulation examples are given. The solid curves in Figs. 1 and 2 represent arbitrary functions selected by us. The dotted curves are approximation curves obtained with wavelet networks given by g (x). Fies. 1 and 2 appear to show that the approximations are satisfactory as predicted by our theorem.