Pseudorandom vector generation by the multiple-recursive matrix method
HTML articles powered by AMS MathViewer
- by Harald Niederreiter PDF
- Math. Comp. 64 (1995), 279-294 Request permission
Abstract:
Pseudorandom vectors are of importance for parallelized simulation methods. In this paper we carry out an in-depth analysis of the multiple-recursive matrix method for the generation of uniform pseudorandom vectors which was introduced in an earlier paper of the author. We study, in particular, the periodicity properties, the lattice structure, and the behavior under the serial test for sequences of pseudorandom vectors generated by this method.References
- Lothar Afflerbach and Holger Grothe, The lattice structure of pseudo-random vectors generated by matrix generators, J. Comput. Appl. Math. 23 (1988), no. 1, 127–131. MR 952072, DOI 10.1016/0377-0427(88)90338-X
- Stuart L. Anderson, Random number generators on vector supercomputers and other advanced architectures, SIAM Rev. 32 (1990), no. 2, 221–251. MR 1056053, DOI 10.1137/1032044
- V. C. Bhavsar and J. R. Isaac, Design and analysis of parallel Monte Carlo algorithms, SIAM J. Sci. Statist. Comput. 8 (1987), no. 1, S73–S95. Parallel processing for scientific computing (Norfolk, Va., 1985). MR 873952, DOI 10.1137/0908014
- William F. Eddy, Random number generators for parallel processors, J. Comput. Appl. Math. 31 (1990), no. 1, 63–71. Random numbers and simulation (Lambrecht, 1988). MR 1068149, DOI 10.1016/0377-0427(90)90336-X
- Jürgen Eichenauer and Jürgen Lehn, A nonlinear congruential pseudorandom number generator, Statist. Hefte 27 (1986), no. 4, 315–326. MR 877295
- Donald E. Knuth, The art of computer programming. Vol. 2, 2nd ed., Addison-Wesley Series in Computer Science and Information Processing, Addison-Wesley Publishing Co., Reading, Mass., 1981. Seminumerical algorithms. MR 633878 P. L’Ecuyer, Random numbers for simulation, Comm. ACM 33 (1990), no. 10, 85-97.
- Pierre L’Ecuyer, Uniform random number generation, Ann. Oper. Res. 53 (1994), 77–120. Simulation and modeling. MR 1310607, DOI 10.1007/BF02136827
- Rudolf Lidl and Harald Niederreiter, Finite fields, 2nd ed., Encyclopedia of Mathematics and its Applications, vol. 20, Cambridge University Press, Cambridge, 1997. With a foreword by P. M. Cohn. MR 1429394 M. Matsumoto and Y. Kurita, Twisted GFSR generators, ACM Trans. Modeling Comput. Simulation 2 (1992), 179-194.
- Harald Niederreiter, Pseudo-random numbers and optimal coefficients, Advances in Math. 26 (1977), no. 2, 99–181. MR 476679, DOI 10.1016/0001-8708(77)90028-7
- Harald Niederreiter, The serial test for pseudorandom numbers generated by the linear congruential method, Numer. Math. 46 (1985), no. 1, 51–68. MR 777824, DOI 10.1007/BF01400255
- H. Niederreiter, Statistical independence properties of pseudorandom vectors produced by matrix generators, J. Comput. Appl. Math. 31 (1990), no. 1, 139–151. Random numbers and simulation (Lambrecht, 1988). MR 1068157, DOI 10.1016/0377-0427(90)90345-Z
- Harald Niederreiter, Finite fields and their applications, Contributions to general algebra, 7 (Vienna, 1990) Hölder-Pichler-Tempsky, Vienna, 1991, pp. 251–264. MR 1143089 —, Nonlinear methods for pseudorandom number and vector generation, Simulation and Optimization (G. Pflug and U. Dieter, eds.), Lecture Notes in Econom. Math. Systems, vol. 374, Springer, Berlin, 1992, pp. 145-153.
- Harald Niederreiter, Random number generation and quasi-Monte Carlo methods, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 63, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992. MR 1172997, DOI 10.1137/1.9781611970081
- Harald Niederreiter, Factorization of polynomials and some linear-algebra problems over finite fields, Linear Algebra Appl. 192 (1993), 301–328. Computational linear algebra in algebraic and related problems (Essen, 1992). MR 1236747, DOI 10.1016/0024-3795(93)90247-L —, Pseudorandom vector generation by the inversive method, ACM Trans. Modeling Comput. Simulation (to appear).
- Harald Niederreiter, The multiple-recursive matrix method for pseudorandom number generation, Finite Fields Appl. 1 (1995), no. 1, 3–30. MR 1334623, DOI 10.1006/ffta.1995.1002
- Brian D. Ripley, Stochastic simulation, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics, John Wiley & Sons, Inc., New York, 1987. MR 875224, DOI 10.1002/9780470316726
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Math. Comp. 64 (1995), 279-294
- MSC: Primary 65C10; Secondary 11K45
- DOI: https://doi.org/10.1090/S0025-5718-1995-1265018-4
- MathSciNet review: 1265018