Improved lower bounds for the discrepancy of inversive congruential pseudorandom numbers
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- by Jürgen Eichenauer-Herrmann PDF
- Math. Comp. 62 (1994), 783-786 Request permission
Abstract:
The inversive congruential method with prime modulus for generating uniform pseudorandom numbers is studied. Lower bounds for the discrepancy of k-tuples of successive pseudorandom numbers are established, which improve earlier results of Niederreiter. Moreover, the present proof is substantially simpler than the earlier one.References
- J. Eichenauer-Herrmann, Inversive congruential pseudorandom numbers, Z. Angew. Math. Mech. 73 (1993), no. 7-8, T644–T647. Bericht über die Wissenschaftliche Jahrestagung der GAMM (Leipzig, 1992). MR 1237851, DOI 10.2307/1403647
- Mary Flahive and Harald Niederreiter, On inversive congruential generators for pseudorandom numbers, Finite fields, coding theory, and advances in communications and computing (Las Vegas, NV, 1991) Lecture Notes in Pure and Appl. Math., vol. 141, Dekker, New York, 1993, pp. 75–80. MR 1199823
- Rudolf Lidl and Harald Niederreiter, Finite fields, Encyclopedia of Mathematics and its Applications, vol. 20, Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA, 1983. With a foreword by P. M. Cohn. MR 746963
- Harald Niederreiter, Lower bounds for the discrepancy of inversive congruential pseudorandom numbers, Math. Comp. 55 (1990), no. 191, 277–287. MR 1023766, DOI 10.1090/S0025-5718-1990-1023766-0
- Harald Niederreiter, Recent trends in random number and random vector generation, Ann. Oper. Res. 31 (1991), no. 1-4, 323–345. Stochastic programming, Part II (Ann Arbor, MI, 1989). MR 1118905, DOI 10.1007/BF02204856 —, Nonlinear methods for pseudorandom number and vector generation, Simulation and Optimization (G. Pflug and U. Dieter, eds.), Lecture Notes in Econom. and 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
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Math. Comp. 62 (1994), 783-786
- MSC: Primary 11K45; Secondary 65C10
- DOI: https://doi.org/10.1090/S0025-5718-1994-1216258-0
- MathSciNet review: 1216258