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)
On the L2-discrepancy for anchored boxes
Journal of Complexity
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)
Algorithm 247: Radical-inverse quasi-random point sequence
Communications of the ACM
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
Algorithm 823: Implementing scrambled digital sequences
ACM Transactions on Mathematical Software (TOMS)
I-binomial scrambling of digital nets and sequences
Journal of Complexity
Parallel linear congruential generators with Sophie-Germain moduli
Parallel Computing
Halton Sequences Avoid the Origin
SIAM Review
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
Randomized Gandy-Păun-Rozenberg machines
CMC'10 Proceedings of the 11th international conference on Membrane computing
Tuning the generation of sobol sequence with owen scrambling
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Hi-index | 0.00 |
Quasi-Monte Carlo (QMC) methods are now widely used in scientific computation, especially in estimating integrals over multidimensional domains. One advantage of QMC is that it is easy to parallelize applications, and so the success of any parallel QMC application depends crucially on the quality of parallel quasirandom sequences used. Much of the recent work dealing with parallel QMC methods has been aimed at splitting a single quasirandom sequence into many subsequences. In contrast with this perspective to concentrate on breaking one sequence up, this paper proposes an alternative approach to generating parallel sequences for QMC. This method generates parallel sequences of quasirandom numbers via scrambling. The exact meaning of scrambling depends on the type of parallel quasirandom numbers. In general, we seek to randomize the generator matrix for each quasirandom number generator. Specifically, this paper will discuss how to parallelize the Halton sequence via scrambling. The proposed scheme for generating parallel random number streams is especially good for heterogeneous and unreliable computing environments.