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Improved lower bounds for the discrepancy of inversive congruential pseudorandom numbers

Author: Jürgen Eichenauer-Herrmann
Journal: Math. Comp. 62 (1994), 783-786
MSC: Primary 11K45; Secondary 65C10
MathSciNet review: 1216258
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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 [Enhancements On Off] (What's this?)

  • [1] J. Eichenauer-Herrmann, Inversive congruential pseudorandom numbers: a tutorial, Internat. Statist. Rev. 60 (1992), 167-176. MR 1237851
  • [2] M. Flahive and H. Niederreiter, On inversive congruential generators for pseudorandom numbers, Proc. Internat. Conf. on Finite Fields (Las Vegas, 1991), Dekker, New York, 1992, pp. 75-80. MR 1199823 (94a:11117)
  • [3] R. Lidl and H. Niederreiter, Finite fields, Addison-Wesley, Reading, MA, 1983. MR 746963 (86c:11106)
  • [4] H. Niederreiter, Lower bounds for the discrepancy of inversive congruential pseudorandom numbers, Math. Comp. 55 (1990), 277-287. MR 1023766 (91e:65016)
  • [5] -, Recent trends in random number and random vector generation, Ann. Oper. Res. 31 (1991), 323-345. MR 1118905 (92h:65010)
  • [6] -, 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.
  • [7] -, Random number generation and quasi-Monte Carlo methods, SIAM, Philadelphia, PA, 1992. MR 1172997 (93h:65008)

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Keywords: Uniform pseudorandom numbers, inversive congruential method, prime modulus, discrepancy
Article copyright: © Copyright 1994 American Mathematical Society

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