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Volume 29, Issue 2
Constructive Approximation by Superposition of Sigmoidal Functions

D. Costarelli & R. Spigler

DOI: 10.4208/ata.2013.v29.n2.8

Anal. Theory Appl., 29 (2013), pp. 169-196.

Published online: 2013-06

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  • 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.

  • Keywords

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

  • AMS Subject Headings

41A25, 41A30

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{ATA-29-169, author = {D. Costarelli and R. Spigler}, title = {Constructive Approximation by Superposition of Sigmoidal Functions}, journal = {Analysis in Theory and Applications}, year = {2013}, volume = {29}, number = {2}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2013.v29.n2.8}, url = {http://global-sci.org/intro/article_detail/ata/4525.html} }
TY - JOUR T1 - Constructive Approximation by Superposition of Sigmoidal Functions AU - D. Costarelli & R. Spigler JO - Analysis in Theory and Applications VL - 2 SP - 169 EP - 196 PY - 2013 DA - 2013/06 SN - 29 DO - http://doi.org/10.4208/ata.2013.v29.n2.8 UR - https://global-sci.org/intro/article_detail/ata/4525.html KW - Sigmoidal functions, multivariate approximation, $L^p$ approximation, neural networks, radial basis functions. AB -

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.

D. Costarelli and R. Spigler. (2013). Constructive Approximation by Superposition of Sigmoidal Functions. Analysis in Theory and Applications. 29 (2). 169-196. doi:10.4208/ata.2013.v29.n2.8
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