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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Average equidistribution properties of compound nonlinear congruential pseudorandom numbers
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by Jürgen Eichenauer-Herrmann and Gerhard Larcher PDF
Math. Comp. 66 (1997), 363-372 Request permission


The present paper deals with the compound nonlinear congruential method for generating uniform pseudorandom numbers, which has been introduced recently. Equidistribution properties of the generated sequences over parts of the period are studied, based on the discrepancy of the corresponding point sets. Upper and lower bounds for the average value of these discrepancies are established, which are essentially best possible. These results show that the average equidistribution behavior of compound nonlinear congruential pseudorandom numbers fits well the equidistribution properties of true random numbers. The method of proof relies heavily on estimates of the average value of incomplete exponential sums.
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Additional Information
  • Jürgen Eichenauer-Herrmann
  • Affiliation: Fachbereich Mathematik, Technische Hochschule Darmstadt, Schloßgartenstraße 7, D–64289 Darmstadt, F.R. Germany
  • Gerhard Larcher
  • Affiliation: Institut für Mathematik, Universität Salzburg, Hellbrunner Straße 34, A–5020 Salzburg, Austria
  • Email:
  • Received by editor(s): July 13, 1995
  • © Copyright 1997 American Mathematical Society
  • Journal: Math. Comp. 66 (1997), 363-372
  • MSC (1991): Primary 65C10; Secondary 11K45
  • DOI:
  • MathSciNet review: 1377661