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A Monte Carlo computation of polynomial approximations on a hypercube

Sylvain Maire 1, 2 
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
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.
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Submitted on : Tuesday, February 28, 2017 - 10:25:24 PM
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Sylvain Maire. A Monte Carlo computation of polynomial approximations on a hypercube. Comptes Rendus. Mathématique, Académie des sciences (Paris), 2003, 336 (2), pp.185-190. ⟨10.1016/S1631-073X(03)00014-1⟩. ⟨hal-01479854⟩



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