Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
A note on polynomial arithmetic analogue of Halton sequences
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Quasirandom number generators for parallel Monte Carlo algorithms
Journal of Parallel and Distributed Computing
Computational investigations of low-discrepancy sequences
ACM Transactions on Mathematical Software (TOMS)
Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators
ACM Transactions on Mathematical Software (TOMS)
Algorithm 806: SPRNG: a scalable library for pseudorandom number generation
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
The effective dimension and quasi-Monte Carlo integration
Journal of Complexity
I-binomial scrambling of digital nets and sequences
Journal of Complexity
Parallel linear congruential generators with Sophie-Germain moduli
Parallel Computing
Efficient simulated maximum likelihood with an application to online retailing
Statistics and Computing
On the optimal Halton sequence
Mathematics and Computers in Simulation
A scalable low discrepancy point generator for parallel computing
ISPA'04 Proceedings of the Second international conference on Parallel and Distributed Processing and Applications
Quasi-random approach in the grid application SALUTE
PPAM'09 Proceedings of the 8th international conference on Parallel processing and applied mathematics: Part II
Tuning the generation of sobol sequence with owen scrambling
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
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Much of the recent work on parallelizing quasi-Monte Carlo methods has been aimed at splitting a quasirandom sequence into many subsequences which are then used independently on the various parallel processes. This method works well for the parallelization of pseudorandom numbers, but due to the nature of quality in quasirandom numbers, this technique has many drawbacks. In contrast, this paper proposes an alternative approach for generating parallel quasirandom sequences via scrambling. The exact meaning of the digit scrambling we use depends on the mathematical details of the quasirandom number sequence's method of generation. The Faure sequence is scramble by modifying the generator matrices in the definition. Thus, we not only obtain the expected near-perfect speedup of the naturally parallel Monte Carlo methods, but the errors in the parallel computation is even smaller than if the computation were done with the same quantity of quasirandom numbers using the original Faure sequence.