Constructive Approximation by Superposition of Sigmoidal Functions

被引：3

作者：

Danilo Costarelli ^{[1
]}

Renato Spigler ^{[1
]}

机构：

[1] Dipartimento di Matematica, Universita` "Roma Tre", 1, Largo S. Leonardo Murialdo, 00146 Rome, Italy

来源：

Analysis in Theory and Applications | 2013年 / 29卷 / 02期

关键词：

Sigmoidal functions; multivariate approximation; L p approximation; neural net- works; radial basis functions;

D O I：

暂无

中图分类号：

O174 [函数论];

学科分类号：

070104 ;

摘要：

In this paper, a constructive theory is developed for approximating functions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the L p norm. Results for the simultaneous approximation, with the same order of accuracy, of a function and its derivatives (whenever these exist), are obtained. The relation with neural networks and radial basis functions approximations is discussed. Numerical examples are given for the purpose of illustration.

引用

页码：169 / 196

页数：28

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