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

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...

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Bibliographic Details
Main Author: Giorgio Gnecco
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/806945
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Summary: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.
ISSN:1110-757X
1687-0042