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Journal Articles Journal of Computational and Applied Mathematics Year : 2003

An iterative computation of approximations on Korobov-like spaces

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.

Dates and versions

hal-01479853 , version 1 (28-02-2017)

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Sylvain Maire. An iterative computation of approximations on Korobov-like spaces. Journal of Computational and Applied Mathematics, 2003, 157 (2), pp.261-281. ⟨10.1016/S0377-0427(03)00410-2⟩. ⟨hal-01479853⟩
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