A Quasi-Monte Carlo Method for Integration with Improved Convergence

Authors:
Aneta Karaivanova;Ivan Dimov;Sofiya Ivanovska
Affiliations:
-;-;-
Venue:
LSSC '01 Proceedings of the Third International Conference on Large-Scale Scientific Computing-Revised Papers
Year:
2001

Citing 4
Cited 0

Random number generation and quasi-Monte Carlo methods

Random number generation and quasi-Monte Carlo methods
Quasi-Monte Carlo integration

Journal of Computational Physics
Monto Carlo extension of quasi-Monte Carlo

Proceedings of the 30th conference on Winter simulation
Smoothness and dimension reduction in Quasi-Monte Carlo methods

Mathematical and Computer Modelling: An International Journal

Quantified Score

Hi-index	0.00

Visualization

Abstract

Quasi-Monte Carlo methods are based on the idea that random Monte Carlo techniques can often be improved by replacing the underlying source of random numbers with a more uniformly distributed deterministic sequence. Quasi-Monte Carlo methods often include standard approaches of variance reduction, although such techniques do not necessarily directly translate. In this paper we present a quasi-Monte Carlo method for integration that combines a separation of the domain into uniformly small subdomains with the approach of importance sampling. Theoretical estimates for the error bounds and the convergence rate are established. A large number of numerical tests of the proposed method are presented and compared with crude Monte Carlo and weighted uniform sampling. All methods are realized using pseudorandom numbers, and Sobol, Halton and Faure quasirandom sequences. The numerical results confirm the improved convergence of the proposed method when the integrand has bounded derivatives.