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Constructive Approximation by Superposition of Sigmoidal Functions

Constructive Approximation by Superposition of Sigmoidal Functions
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Year:    2013

Analysis in Theory and Applications, Vol. 29 (2013), Iss. 2 : pp. 169–196

Abstract

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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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2013.v29.n2.8

Analysis in Theory and Applications, Vol. 29 (2013), Iss. 2 : pp. 169–196

Published online:    2013-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    28

Keywords:    Sigmoidal functions multivariate approximation $L^p$ approximation neural networks radial basis functions.

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