Polynomial approximations of multivariate smooth functions from quasi-random data

Authors:
Sylvain Maire
Affiliations:
ISITV, Université de Toulon et du Var, Avenue G, Pompidou BP 56 - 83262, La Valette du Var, Cedex, France. maire@univ-tln.fr
Venue:
Statistics and Computing
Year:
2004

Citing 4
Cited 3

Monte Carlo methods. Vol. 1: basics

Monte Carlo methods. Vol. 1: basics
Random number generation and quasi-Monte Carlo methods

Random number generation and quasi-Monte Carlo methods
A space quantization method for numerical integration

Journal of Computational and Applied Mathematics
An iterative computation of approximations on Korobov-like spaces

Journal of Computational and Applied Mathematics

Quasi-Monte Carlo quadratures for multivariate smooth functions

Applied Numerical Mathematics
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

Quantified Score

Hi-index	0.00

Visualization

Abstract

We improve a Monte Carlo algorithm which computes accurate approximations of smooth functions on multidimensional Tchebychef polynomials by using quasi-random sequences. We first show that the convergence of the previous algorithm is twice faster using these sequences. Then, we slightly modify this algorithm to make it work from a single set of random or quasi-random points. This especially leads to a Quasi-Monte Carlo method with an increased rate of convergence for numerical integration.