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.
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页码：169 / 196
页数：28
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