Algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
Techniques for parallel quasi-Monte Carlo integration with digital sequences and associated problems
Mathematics and Computers in Simulation - IMACS sponsored Special issue on the second IMACS seminar on Monte Carlo methods
Monte Carlo and Quasi-Monte Carlo Algorithms for the Barker-Ferry Equation with Low Complexity
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
Generalized Halton sequences in 2008: A comparative study
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Quasi-random approach in the grid application SALUTE
PPAM'09 Proceedings of the 8th international conference on Parallel processing and applied mathematics: Part II
Monte Carlo algorithms for evaluating Sobol' sensitivity indices
Mathematics and Computers in Simulation
A quasi-monte carlo method for an elastic electron back-scattering problem
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
A superconvergent monte carlo method for multiple integrals on the grid
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
Evolutionary optimization of low-discrepancy sequences
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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The Halton sequences are one of the most popular lowdiscrepancy sequences, used for calculating multi-dimensional integrals or in quasi-Monte Carlo simulations. Various techniques for their randomization exist. One of the authors proved that for one such modification an estimate of the discrepancy with a very small constant before the leading term can be proved. In this paper we describe an efficient algorithm for generating these sequences on computers and show timing results, demonstrating the efficiency of the algorithm. We also compare the integration error of these sequences with that of the classical Halton sequences on families of functions widely used for such benchmarking purposes. The results demonstrate that the modified Halton sequences can be used successfully in quasi-Monte Carlo methods.