Theoretical analyses of forward and backward heuristics of multiple recursive random number generators

This article focuses on heuristic algorithms that are capable of finding multiple recursive generators (MRGs) with maximum spectral value criterion in a short period of time. Two promising algorithms, provided by Kao and Tang, are the forward and backward heuristics. Here we provide a deep understanding of the forward and backward heuristics for an MRG. The forward heuristic finds a sequence of partial sets of multipliers that lead toward a better spectral value. For the second-order MRGs, the performance of the backward heuristic theoretically outperforms that of the forward heuristic. The effectiveness of the backward heuristic is numerically confirmed by the experiments we present.