An iterative computation of approximations on Korobov-like spaces

Sylvain Maire (1, 2)

1 TOSCA
2 MNC - Modélisation Numérique et Couplages

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.

Keywords: Monte Carlo method; Iterative algorithm; Polynomial approximations; Korobov spaces; Numerical integration

Domains: Computer Science [cs]; Signal and Image Processing

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⟩