Numerische Mathematik

, Volume 46, Issue 1, pp 51–68 | Cite as

The serial test for pseudo-random numbers generated by the linear congruential method

  • Harald Niederreiter
Article

Summary

We consider the linear congruential method for pseudo-random number generation and establish effective criteria for the choice of parameters in this method which guarantee statistical almost-independence of successive pseudo-random numbers. Applications to numerical integration are also discussed.

Subject Classifications

AMS 65C10 65D30 CR: G3 

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References

  1. 1.
    Borosh, I., Niederreiter, H.: Optimal multipliers for pseudo-random number generation by the linear congruential method BIT23, 65–74 (1983)Google Scholar
  2. 2.
    Dieter, U.: Pseudo-random numbers: The exact distribution of pairs. Math. Comput.25, 855–883 (1971)Google Scholar
  3. 3.
    Hardy, G.H., Wright, E.M.: An introduction to the theory of numbers. 4th ed. Oxford: Clarendon Press 1960Google Scholar
  4. 4.
    Knuth, D.E.: The art of computer programming, vol. 2: Seminumerical algorithms, 2nd ed. Reading, MA: Addison-Wesley 1981Google Scholar
  5. 5.
    Kuipers, L., Niederreiter, H.: Uniform distribution of sequences. New York: Wiley-Interscience 1974Google Scholar
  6. 6.
    Niederreiter, H.: On the distribution of pseudo-random numbers generated by the linear congruential method. Math. Comput.26, 793–795 (1972)Google Scholar
  7. 7.
    Niederreiter, H.: On the distribution of pseudo-random numbers generated by the linear congruential method. II. Math. Comput.28, 1117–1132 (1974)Google Scholar
  8. 8.
    Niederreiter, H.: On the distribution of pseudo-random numbers generated by the linear congruential method. III. Math. Comput.30, 571–597 (1976)Google Scholar
  9. 9.
    Niederreiter, H.: Pseudo-random numbers and optimal coefficients. Adv. Math.26, 99–181 (1977)Google Scholar
  10. 10.
    Niederreiter, H.: The serial test for linear congruential pseudo-random numbers. Bull. Amer. Math. Soc.84, 273–274 (1978)Google Scholar
  11. 11.
    Niederreiter, H.: Quasi-Monte Carlo methods and pseudo-random numbers. Bull. Am. Math. Soc.84, 957–1041 (1978)Google Scholar
  12. 12.
    Niederreiter, H.: Statistical tests for linear congruential pseudo-random numbers. In: COMP-STAT 1978: Proceedings in computational statistics (Leiden, 1978), pp. 398–404. Vienna: Physica-Verlag 1978Google Scholar
  13. 13.
    Niederreiter, H.: Nombres pseudo-aléatoires et équirépartition. Astérisque61, 155–164 (1979)Google Scholar
  14. 14.
    Niederreiter, H.: Statistical tests for Tausworthe pseudo-random numbers. In: Probability and statistical inference (W. Grossmann, G.C. Pflug, W. Wertz, eds.), pp. 265–274. Dordrecht: Reidel 1982Google Scholar
  15. 15.
    Niederreiter, H.: Optimal multipliers for linear congruential pseudo-random numbers: The decimal case. In: Proc. Third Panonian Symp. Math. Statistics (Visegrád, 1982) pp. 255–269. Budapest: Akadémi ai Kiadó 1983Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Harald Niederreiter
    • 1
  1. 1.Mathematical InstituteAustrian Academy of SciencesViennaAustria

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