SYSTEMATIC SEARCHES FOR GOOD MULTIPLE RECURSIVE RANDOM NUMBER GENERATORS

This paper proposes two systematic ways to search for good MRGs, in te rms of the lattice structure, in a partially exhaustive manner. One is a backward method and the other is a forward method. Several good MRG s of order 1, 2, and 3, with modulus 2(31)-1, found from these two met hods are presented. When computational efficiency is the major concern , another group of MRGs where the approximate factoring technique can be applied are generated. Roughly speaking, the execution time of the k-term MRG is k times that of the one-term PMMCG. By adapting to the a pproximate factoring technique, there is a reduction of around 40% in execution time, with a trade-off of less satisfactory lattice structur e of the RNs produced. These generators should be useful for computer simulation studies with different objectives, and the proposed methods are suitable for finding good MRGs of higher order. (C) 1997 Elsevier Science Ltd.