Efficient Generation of Parallel Quasirandom Faure Sequences Via Scrambling

摘要

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.