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Optimal multipliers for pseudo-random number generation by the linear congruential method

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Abstract

A systematic search method is employed to find multipliers for linear congruential pseudo-random number generation which are optimal with respect to statistical independence of pairs of successive pseudo-random numbers. Tables of such optimal multipliers corresponding to moduli 2n,n ≦ 35, are included.

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References

  1. I. Borosh,Rational continued fractions with small partial quotients, preprint.

  2. T. W. Cusick,Continuants with bounded digits, Mathematika 24 (1977), 166–172.

    Google Scholar 

  3. U. Dieter,Pseudo-random numbers: The exact distribution of pairs, Math. Comp. 25 (1971), 855–883.

    Google Scholar 

  4. B. Jansson,Random Number Generators, Almqvist & Wiksell, Stockholm (1966).

    Google Scholar 

  5. D. E. Knuth,The Art of Computer Programming, Vol. 2:Seminumerical Algorithms, Addison-Wesley, Reading, Mass. (1969).

    Google Scholar 

  6. L. Kuipers and H. Niederreiter,Uniform Distribution of Sequences, Wiley-Interscience, New York (1974).

    Google Scholar 

  7. H. Niederreiter,Statistical independence of linear congruential pseudo-random numbers, Bull. Amer. Math. Soc. 82 (1976), 927–929.

    Google Scholar 

  8. H. Niederreiter,Pseudo-random numbers and optimal coefficients, Advances in Math. 26 (1977), 99–181.

    Article  Google Scholar 

  9. H. Niederreiter,The serial test for linear congruential pseudo-random numbers, Bull. Amer. Math. Soc. 84 (1978), 273–274.

    Google Scholar 

  10. H. Niederreiter,Quasi-Monte Carlo methods and pseudo-random numbers, Bull. Amer. Math. Soc. 84 (1978), 957–1041.

    Google Scholar 

  11. S. K. Zaremba, La méthode des “bons treillis” pour le calcul des intégrales multiples, Applications of Number Theory to Numerical Analysis (S. K. Zaremba, ed.), 39–119, Academic Press, New York (1972).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Texas A & M University, 77840, College Station, Texas, USA

    Itshak Borosh & Harald Niederreiter

  2. Kommission für Mathematik, Österreichische Akademie der Wissenschaften, Dr. Ignaz-Seipel-Platz, A-1010, Wien, Austria

    Itshak Borosh & Harald Niederreiter

Authors
  1. Itshak Borosh
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  2. Harald Niederreiter
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Additional information

This author was partially supported by NSF Grant MCS 76-06092.

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Borosh, I., Niederreiter, H. Optimal multipliers for pseudo-random number generation by the linear congruential method. BIT 23, 65–74 (1983). https://doi.org/10.1007/BF01937326

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  • DOI: https://doi.org/10.1007/BF01937326

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