摘要
研究单隐层神经网络逼近问题．以最佳多项式逼近为度量,用构造性方法估计单隐层神经网络逼近连续函数的速度．所获结果表明:对定义在紧集上的任何连续函数,均可以构造一个单隐层神经网络逼近该函数,并且其逼近速度不超过该函数的最佳多项式逼近的二倍．
The problem of approximation for neural networks with single hidden layer is studied in this paper. With the best polynomial approximation as a metric, the rate of approximation of the neural networks with single hidden layer to a continuous function is estimated by using a constructive approach. The result obtained shows that for any continuous function defined a compact set, a neural network with single networks can be constructed to approximate the function, and the rate of approximation do not exceed the double of the best polynomial approximation of the function.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2007年第2期385-392,共8页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金(60473034
70571024)
国家博士后科学基金(20040350225)
浙江省教育厅科研重点基金(20060543)
关键词
单隐层神经网络
逼近速度
最佳多项式逼近
neural networks with single hidden layer
rate of approximation
best polynomial approximation
