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.