Journal of Applied Mathematics

A Comparison between Fixed-Basis and Variable-Basis Schemes for Function Approximation and Functional Optimization

Giorgio Gnecco

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Abstract

Fixed-basis and variable-basis approximation schemes are compared for the problems of function approximation and functional optimization (also known as infinite programming). Classes of problems are investigated for which variable-basis schemes with sigmoidal computational units perform better than fixed-basis ones, in terms of the minimum number of computational units needed to achieve a desired error in function approximation or approximate optimization. Previously known bounds on the accuracy are extended, with better rates, to families of d -variable functions whose actual dependence is on a subset of d d variables, where the indices of these d variables are not known a priori.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 806945, 17 pages.

Dates
First available in Project Euclid: 17 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1350479408

Digital Object Identifier
doi:10.1155/2012/806945

Mathematical Reviews number (MathSciNet)
MR2872340

Zentralblatt MATH identifier
1242.49064

Citation

Gnecco, Giorgio. A Comparison between Fixed-Basis and Variable-Basis Schemes for Function Approximation and Functional Optimization. J. Appl. Math. 2012 (2012), Article ID 806945, 17 pages. doi:10.1155/2012/806945. https://projecteuclid.org/euclid.jam/1350479408


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