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

作者：Gnecco Giorgio^*

来源：Journal of Applied Mathematics, 2012, 806945.

DOI：10.1155/2012/806945

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%26apos; %26lt;%26lt; d variables, where the indices of these d%26apos; variables are not known a priori.

• 出版日期2012