%0 Journal Article
%T A Comparison between Fixed-Basis and Variable-Basis Schemes for Function Approximation and Functional Optimization
%A Giorgio Gnecco
%J Journal of Applied Mathematics
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/806945
%X 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 -variable functions whose actual dependence is on a subset of ­å£¿ variables, where the indices of these ­å variables are not known a priori.
%U http://www.hindawi.com/journals/jam/2012/806945/