Quasi-random sequences and their discrepancies
SIAM Journal on Scientific Computing
Quasirandom number generators for parallel Monte Carlo algorithms
Journal of Parallel and Distributed Computing
On the L2-discrepancy for anchored boxes
Journal of Complexity
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
Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates
Mathematics and Computers in Simulation - IMACS sponsored Special issue on the second IMACS seminar on Monte Carlo methods
Remark on algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
The effective dimension and quasi-Monte Carlo integration
Journal of Complexity
Algorithm 823: Implementing scrambled digital sequences
ACM Transactions on Mathematical Software (TOMS)
Parallel Computing on Heterogeneous Networks
Parallel Computing on Heterogeneous Networks
Grid Computing: Making the Global Infrastructure a Reality
Grid Computing: Making the Global Infrastructure a Reality
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One major advantage of Monte Carlo methods is that they are usually very easy to parallelise; this leads us to all Monte Carlo methods naturally parallel algorithms. This is, in principal, also true of quasi-Monte Carlo (QMC) methods. However, the successful parallel implementation of a QMC application depends crucially on various quality aspects of the parallel quasirandom sequences used. Much of the recent work on parallelising QMC 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 parallelisation 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 (Soboĺ) sequences by independent sequences for each processor. The proposed scheme for generating independent parallel sequences is especially suitable for heterogeneous and unreliable computing environments.