Quasi-Monte Carlo quadratures for multivariate smooth functions

Authors:
Sylvain Maire;Christophe De Luigi
Affiliations:
ISITV, Université du Sud Toulon-Var, Avenue G. Pompidou BP 56, 83262 La Valette du Var cedex, France;ISITV, Université du Sud Toulon-Var, Avenue G. Pompidou BP 56, 83262 La Valette du Var cedex, France
Venue:
Applied Numerical Mathematics
Year:
2006

Citing 8
Cited 0

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
A space quantization method for numerical integration

Journal of Computational and Applied Mathematics
My dream quadrature rule

Journal of Complexity
An iterative computation of approximations on Korobov-like spaces

Journal of Computational and Applied Mathematics
Polynomial approximations of multivariate smooth functions from quasi-random data

Statistics and Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We compute approximations of multivariate smooth functions by fitting random and quasi-random data to reduced size Tchebychef polynomial approximation models. We discuss the optimization of the data used in the least square method by testing several quasi-random sequences. Points built from optimal quadratic quantization are especially efficient. Very accurate approximation type quadrature formulas are obtained avoiding the usual periodisation problems when using lattices rules. Some numerical tests confirm the efficiency of our quadratures compared to standard methods.