Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Pseudorandom vector generation
by the compound inversive method

Author: Frank Emmerich
Journal: Math. Comp. 65 (1996), 749-760
MSC (1991): Primary 65C10; Secondary 11K45
MathSciNet review: 1333311
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Pseudorandom vectors are of importance for parallelized simulation methods. In this paper a detailed analysis of the compound inversive method for the generation of $k$-dimensional uniform pseudorandom vectors, a vector analog of the compound inversive method for pseudorandom number generation, is carried out. In particular, periodicity properties and statistical independence properties of the generated sequences are studied based on the discrete discrepancy of $s$-tuples of successive terms in the sequence. The results show that the generated sequences have attractive statistical independence properties for pseudorandom vectors of dimensions $k\leq 4$.

References [Enhancements On Off] (What's this?)

  • 1. J. Eichenauer and J. Lehn, A non-linear congruential pseudorandom number generator, Statist. Hefte 27 (1986), 315--326. MR 88i:65014
  • 2. J. Eichenauer-Herrmann, Inversive congruential pseudorandom numbers: a tutorial, Internat. Statist. Rev. 60 (1992), 167--176.
  • 3. ------, On generalized inversive congruential pseudorandom numbers, Math. Comp. 63 (1994), 293--299. MR 94k:11088
  • 4. ------, Pseudorandom number generation by nonlinear methods, Internat. Statist. Rev. 63 (1995), 247--255.
  • 5. M. Flahive and H. Niederreiter, On inversive congruential generators for pseudorandom numbers, Finite Fields, Coding Theory, and Advances in Communications and Computing (G.L. Mullen and P.J.-S. Shiue, eds.), Dekker, New York, 1993, pp. 75--80. MR 94a:11117
  • 6. J. Kiefer, On large deviations of the empiric d.f. of vector chance variables and a law of the iterated logarithm, Pacific J. Math. 11 (1961), 649--660. MR 24:A1732
  • 7. R. Lidl and H. Niederreiter, Finite fields, Addison-Wesley, Reading, MA, 1983. MR 86c:11106
  • 8. H. Niederreiter, Pseudo-random numbers and optimal coefficients, Adv. in Math. 26 (1977), 99--181. MR 57:16238
  • 9. ------, Finite fields and their applications, Contributions to General Algebra 7 (D. Dorninger, G. Eigenthaler, H. K. Kaiser, and W. B. Müller, eds.), Teubner, Stuttgart, 1991, pp. 251--264. MR 92j:11146
  • 10. ------, 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.
  • 11. ------, Finite fields, pseudorandom numbers, and quasirandom points, Finite Fields, Coding Theory, and Advances in Communications and Computing (G. L. Mullen and P.J.-S. Shiue, eds.), Dekker, New York, 1993, pp. 375--394. MR 94a:11121
  • 12. ------, Random number generation and quasi-Monte Carlo methods, SIAM, Philadelphia, PA, 1992. MR 93h:65008
  • 13. ------, Pseudorandom numbers and quasirandom points, Z. Angew. Math. Mech. 73 (1993), T648-T652. CMP 94:01
  • 14. ------, Pseudorandom vector generation by the inversive method, ACM Trans. Modeling and Computer Simulation 4 (1994), 191--212.

Similar Articles

Retrieve articles in Mathematics of Computation of the American Mathematical Society with MSC (1991): 65C10, 11K45

Retrieve articles in all journals with MSC (1991): 65C10, 11K45

Additional Information

Frank Emmerich
Affiliation: Fachbereich Mathematik, AG9, Technische Hochschule Darmstadt, Schloßgartenstraße 7, D-64289 Darmstadt, Germany

Keywords: Uniform pseudorandom numbers, uniform pseudorandom vectors, inversive method, compound inversive method, statistical independence, discrete discrepancy, exponential sums
Received by editor(s): August 1, 1994
Article copyright: © Copyright 1996 American Mathematical Society

American Mathematical Society