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

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  • Giorgio Gnecco

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.

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  • Giorgio Gnecco, 2012. "A Comparison between Fixed-Basis and Variable-Basis Schemes for Function Approximation and Functional Optimization," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, January.
    • Handle: RePEc:hin:jnljam:806945
    DOI: 10.1155/2012/806945
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    Cited by:

    1. Pedro Duarte Gomes, 2024. "Mathematics of Differential Machine Learning in Derivative Pricing and Hedging," Papers 2405.01233, arXiv.org.
    2. Tibor Kmet & Maria Kmetova & Ladislav Végh, 2023. "Neural Networks Simulation of Distributed SEIR System," Mathematics, MDPI, vol. 11(9), pages 1-14, April.

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