Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Generating and Testing the Modified Halton Sequences
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
Parallel Importance Separation and Adaptive Monte Carlo Algorithms for Multiple Integrals
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
Measuring the Performance of a Power PC Cluster
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Smoothness and dimension reduction in Quasi-Monte Carlo methods
Mathematical and Computer Modelling: An International Journal
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In this paper we present error and performance analysis of a Monte Carlo variance reduction method for solving multidimensional integrals and integral equations. This method combines the idea of separation of the domain into small subdomains with the approach of importance sampling. The importance separation method is originally described in our previous works [7,9]. Here we present a new variant of this method adding polynomial interpolation in subdomains. We also discuss the performance of the algorithms in comparison with crude Monte Carlo. We propose efficient parallel implementation of the importance separation method for a grid environment and we demonstrate numerical experiments on a heterogeneous grid. Two versions of the algorithm are compared – a Monte Carlo version using pseudorandom numbers and a quasi-Monte Carlo version using the Sobol and Halton low-discrepancy sequences [13,8].