Browsing by Author "Li, Huajiang"

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Design and implementation of efficient and portable Multiple Recursive Generators with few zero coefficients
(2008)
Deng, Lih-Yuan
;
Li, Huajiang
;
Shiau, Jyh-Jen Horng
;
Tsai, Gwei-Hung
;
統計學研究所
DX-k, proposed by Deng and Xu [2003], is a special class of Multiple Recursive Generators (MRGs) where all nonzero coefficients of the k-th order recurrence are equal. In particular, a DX-k generator requires only up to four nonzero coefficients in its recurrence equation, hence is very efficient in computation. However, a random number generator with few nonzero coefficients has a drawback that, when the k-dimensional state vector is close to the zero vector, the subsequent numbers generated may stay within a neighborhood of zero for quite many of them before they can break away from this near-zero land, a property apparently not desirable in the sense of randomness. Consequently, two generated sequences using the same DX generator with nearly identical initial state vectors may not depart from each other quickly enough. To avoid the above potential problem, we consider MRGs with very few zero coefficients. To make such generators efficient and portable, we propose selecting the same nonzero value for all coefficients (with at most one exception) in the recurrence equation. With this feature, the proposed generators can be implemented efficiently via a higher-order recurrence of few zero coefficients. Note that the new class of generators is an opposite of the DX generators in terms of the number of nonzero coefficients. Several such generators with the maximum period have been found via computer search and presented in the paper for ready implementation.
Scalable parallel multiple recursive generators of large order
(2009-01-01)
Deng, Lih-Yuan
;
Li, Huajiang
;
Shiau, Jyh-Jen Horng
;
統計學研究所
;
Institute of Statistics
To speed up the process of performing a large statistical simulation study, it is natural and common to divide the large-scale simulation task into several relatively independent sub-tasks in a way that these sub-tasks can be handled by individual processors in parallel. To obtain a good overall simulation result by synthesizing results from these sub-tasks, it is crucial that good parallel random number generators are used. Thus, designing suitable and independent uniform random number generators for the sub-tasks has become a very important issue in large-scale parallel simulations. Two commonly used uniform random number generators, linear congruential generator (LCG) and multiple recursive generator (MRG), have served as backbone generators for some parallel random number generators constructed in the past. We will discuss some general construction methods. A systematic leapfrog method to automatically choose different multipliers for LCGs to have the maximum-period and a method to construct many maximum-period MRGs from a single MRG are available in the literature. In this paper, we propose to combine both approaches to generate different MRGs "randomly", quickly and automatically. while retaining the maximum-period property. Published by Elsevier B.V.