Un algorithme probabiliste de calcul d'approximations polynômiales sur un hypercube

Abstract

We describe a Monte Carlo method which enables an iterative computation of the L 2 approximation of a function on any orthonormal basis. We use it for the approximation of smooth functions on an hypercube with the help of multidimensional orthogonal polynomial basis containing only few terms. The algorithm is both a tool for approximation and numerical integration. To cite this article: S. Maire, C. R. Acad. Sci. Paris, Ser. I 336 (2003).