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On the distribution of pseudo-random numbers generated by the linear congruential method


Author: Harald Niederreiter
Journal: Math. Comp. 26 (1972), 793-795
MSC: Primary 65C10
DOI: https://doi.org/10.1090/S0025-5718-1972-0326979-5
MathSciNet review: 0326979
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Abstract: The discrepancy of sequences of pseudo-random numbers generated by the linear congruential method is estimated, thereby improving a result of Jagerman. Applications to numerical integration are mentioned.


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

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  • [2] D. L. Jagerman, ``Some theorems concerning pseudo-random numbers,'' Math. Comp., v. 19, 1965, pp. 418-426. MR 32 #1877. MR 0184405 (32:1877)
  • [3] J. F. Koksma, ``A general theorem from the theory of uniform distribution modulo 1,'' Mathematka Zutphen. B, v. 11, 1942, pp. 7-11. (Dutch) MR 7, 370. MR 0015094 (7:370a)
  • [4] H. Niederreiter, ``Methods for estimating discrepancy,'' Proc. Sympos. on Applications of Number Theory to Numerical Analysis (Montreal, 1971), Academic Press, New York, 1972. (To appear.) MR 0354593 (50:7071)
  • [5] H. Niederreiter, ``Almost-arithmetic progressions and uniform distribution,'' Trans. Amer. Math. Soc., v. 161, 1971, pp. 283-292. MR 0284406 (44:1633)
  • [6] H. Niederreiter, ``Discrepancy and convex programming,'' Ann. Mat. Pura Appl., 1972. (To appear.) MR 0389828 (52:10658)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1972-0326979-5
Keywords: Pseudo-random numbers, discrepancy, numerical integration
Article copyright: © Copyright 1972 American Mathematical Society

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