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.