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

D. Costarelli & R. Spigler

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 functionsof one or more variables by superposition of sigmoidal functions. This is donein 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 (wheneverthese exist), are obtained. The relation with neural networks and radial basis functionsapproximations is discussed. Numerical examples are given for the purpose ofillustration.
  • Keywords

Sigmoidal functions multivariate approximation L^p approximation neural networks radial basis functions

  • AMS Subject Headings

41A25 41A30

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COPYRIGHT: © Global Science Press

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@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 functionsof one or more variables by superposition of sigmoidal functions. This is donein 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 (wheneverthese exist), are obtained. The relation with neural networks and radial basis functionsapproximations is discussed. Numerical examples are given for the purpose ofillustration.}, 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 KW - multivariate approximation KW - L^p approximation KW - neural networks KW - radial basis functions AB - In this paper, a constructive theory is developed for approximating functionsof one or more variables by superposition of sigmoidal functions. This is donein 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 (wheneverthese exist), are obtained. The relation with neural networks and radial basis functionsapproximations is discussed. Numerical examples are given for the purpose ofillustration.
D. Costarelli & R. Spigler. (1970). 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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