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An iterative computation of approximations on Korobov-like spaces

Sylvain Maire 1, 2
1 TOSCA
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 : This paper treats the multidimensional application of a previous iterative Monte Carlo algorithm that enables the computation of approximations in $L^2$. The case of regular functions is studied using a Fourier basis on periodised functions, Legendre and Tchebychef polynomial bases. The dimensional effect is reduced by computing these approximations on Korobov-like spaces. Numerical results show the efficiency of the algorithm for both approximation and numerical integration.
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Submitted on : Tuesday, February 28, 2017 - 10:25:22 PM
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Sylvain Maire. An iterative computation of approximations on Korobov-like spaces. Journal of Computational and Applied Mathematics, Elsevier, 2003, 157 (2), pp.261-281. ⟨10.1016/S0377-0427(03)00410-2⟩. ⟨hal-01479853⟩

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