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


Author: Harald Niederreiter
Journal: Math. Comp. 28 (1974), 1117-1132
MSC: Primary 10K05; Secondary 65C10
DOI: https://doi.org/10.1090/S0025-5718-1974-0457391-8
MathSciNet review: 0457391
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Abstract | References | Similar Articles | Additional Information

Abstract: The discrepancy of a sequence of pseudo-random numbers generated by the linear congruential method is estimated for parts of the period which are somewhat larger than the square root of the modulus. Applications to numerical integration are mentioned.


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

  • [1] N. M. KOROBOV, "Trigonometric sums with exponential functions and the distribution of signs in repeating decimals," Mat. Zametki, v. 8, 1970, pp. 641-652, = Math. Notes, v. 8, 1970, pp. 831-837. MR 43 #6165. MR 0280445 (43:6165)
  • [2] N. M. KOROBOV, "On the distribution of digits in periodic fractions," Mat. Sb., v. 89 (131), 1972, pp. 654-670 = Math. USSR Sb., v. 18, 1972, pp. 659-676. MR 0424660 (54:12619)
  • [3] L. KUIPERS & H. NIEDERREITER, Uniform Distribution of Sequences, Wiley, New York, 1974. MR 0419394 (54:7415)
  • [4] L. J. MORDELL, "On the exponential sum $ \Sigma _{x = 1}^X\exp (2\pi i(ax + b{g^x})/h)$," Mathematika, V. 19, 1972, pp. 84-87. MR 0318073 (47:6622)
  • [5] L. J. MORDELL, "A new type of exponential series," Quart. J. Math. (2), v. 23, 1972, pp. 373-374. MR 0319912 (47:8453)
  • [6] H. NIEDERREITER, "Methods for estimating discrepancy," Applications of Number Theory to Numerical Analysis (edited by S. K. Zaremba), Academic Press, New York, 1972, pp. 203-236. MR 0354593 (50:7071)
  • [7] H. NIEDERREITER, "On the distribution of pseudo-random numbers generated by the linear congruential method," Math. Comp., v. 26, 1972, pp. 793-795. MR 0326979 (48:5321)
  • [8] H. NIEDERREITER, "Discrepancy and convex programming," Ann. Mat. Pura Appl. (4), v. 93, 1972, pp. 89-97. MR 0389828 (52:10658)
  • [9] H. NIEDERREITER, "Application of diophantine approximations to numerical integration," Diophantine Approximation and Its Applications (edited by C. F. Osgood), Academic Press, New York, 1973, pp. 129-199. MR 0357357 (50:9825)
  • [10] H. NIEDERREITER & W. PHILIPP, "Berry-Esseen bounds and a theorem of Erdös and Turán on uniform distribution $ \bmod\;1$," Duke Math. J., v. 40, 1973, pp. 633-649. MR 0337873 (49:2642)
  • [11] R. G. STONEHAM, "On the uniform $ \varepsilon $-distribution of residues within the periods of rational fractions with applications to normal numbers," Acta Arith., v. 22, 1973, pp. 371-389. MR 0318091 (47:6640)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1974-0457391-8
Keywords: Pseudo-random numbers, discrepancy, uniform distribution, trigonometric sums, numerical integration
Article copyright: © Copyright 1974 American Mathematical Society

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