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

Giorgio Gnecco

Journal of Applied Mathematics, 2012, vol. 2012, 1-17

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:806945

DOI: 10.1155/2012/806945

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