Efficient Class Matrix Congruential Generator Easily Implemented from Multiple Recursive Generators

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Abstract: Classical random number generators such as Linear Congruential Generators (LCGs) and Multiple Recursive Generators (MRGs) are commonly employed for modern simulation studies. LCGs have a too short period and a too coarse structure to be used as reliable random number generators. Most Matrix Congruential Generators (MCGs) are less applicable due to the inefficiency and the difficulty of deciding the too many coefficients. We propose a class of Efficient Matrix Congruent Generators (EMCGs) including EMCG-1, EMCG-2, EMCG-D and EMCG-G that simultaneously combine k LCGs to form the multiplier matrix of MCGs. We can easily derive the multiple-matrices for all four EMCGs from the corresponding full fixed minimal primitive characteristic polynomials. This makes them easy to implement the results from MRGs without any restrictions on the dimension of a multiple-matrix. We also provide the portable and efficient MAPLE algorithms without using any matrix multiplications for generating the four EMCGs with some selected coefficients that can achieve the high-dimensional uniformity with extreme long cycles.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 14, 2015, Art. #31

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Gwei-Hung Tsai, Der-Jin Chen, Chiou-Hua Lin, "Efficient Class Matrix Congruential Generator Easily Implemented from Multiple Recursive Generators," WSEAS Transactions on Mathematics, vol. 14, pp. 324-334, 2015, DOI:
Gwei-Hung Tsai, Der-Jin Chen, Chiou-Hua Lin. Efficient Class Matrix Congruential Generator Easily Implemented from Multiple Recursive Generators. WSEAS Transactions on Mathematics. 2015;14:324-334.
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