Monte Carlo methods. Vol. 1: basics
Monte Carlo methods. Vol. 1: basics
Lattice methods for multiple integration: theory, error analysis and examples
SIAM Journal on Numerical Analysis
Recursive stratified sampling for multidimensional Monte Carlo integration
Computers in Physics
Imbedded lattice rules for multidimensional integration
SIAM Journal on Numerical Analysis
Numerical Recipes: FORTRAN
Polynomial approximations of multivariate smooth functions from quasi-random data
Statistics and Computing
Quasi-Monte Carlo quadratures for multivariate smooth functions
Applied Numerical Mathematics
Geometric Variance Reduction in Markov Chains: Application to Value Function and Gradient Estimation
The Journal of Machine Learning Research
Geometric variance reduction in Markov chains: application to value function and gradient estimation
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
Quasi-Monte Carlo quadratures for multivariate smooth functions
Applied Numerical Mathematics
Numerical solution of the Poisson equation over hypercubes using reduced Chebyshev polynomial bases
Journal of Computational and Applied Mathematics
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This paper treats the multidimensional application of a previous iterative Monte Carlo algorithm that enables the computation of approximations in L2. 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.