A Comparison between Fixed‐Basis and Variable‐Basis Schemes forFunction Approximation and Functional Optimization
Giorgio Gnecco · Journal of Applied Mathematics · 2012
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.