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 | References | Similar Articles | Additional Information

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.

**[1]**U. Dieter, ``Statistical interdependence of pseudo-random numbers generated by the linear congruential method,''*Proc. Sympos. on Applications of Number Theory to Numerical Analysis*(Montreal, 1971), Academic Press, New York, 1972. (To appear.) MR**0353622 (50:6105)****[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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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