Approximation by Neural Networks with Sigmoidal Functions  

作　　者：Dan Sheng YU 

机构地区：[1]Department of Mathematics,Hangzhou Normal University

出　　处：《Acta Mathematica Sinica,English Series》2013年第10期2013-2026,共14页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.10901044);Qianjiang Rencai Program of Zhejiang Province(Grant No.2010R10101);Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry;Program for Excellent Young Teachers in Hangzhou Normal University

摘　　要：In this paper, we introduce a type of approximation operators of neural networks with sigmodal functions on compact intervals, and obtain the pointwise and uniform estimates of the ap- proximation. To improve the approximation rate, we further introduce a type of combinations of neurM networks. Moreover, we show that the derivatives of functions can also be simultaneously approximated by the derivatives of the combinations. We also apply our method to construct approximation operators of neural networks with sigmodal functions on infinite intervals.In this paper, we introduce a type of approximation operators of neural networks with sigmodal functions on compact intervals, and obtain the pointwise and uniform estimates of the ap- proximation. To improve the approximation rate, we further introduce a type of combinations of neurM networks. Moreover, we show that the derivatives of functions can also be simultaneously approximated by the derivatives of the combinations. We also apply our method to construct approximation operators of neural networks with sigmodal functions on infinite intervals.

关 键 词：Feedforward neural networks sigmoidal functions simultaneous approximation combi-nations 

分 类 号：O174[理学—数学] TP183[理学—基础数学]