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Average equidistribution properties of compound nonlinear congruential pseudorandom numbers

Authors: Jürgen Eichenauer-Herrmann and Gerhard Larcher
Journal: Math. Comp. 66 (1997), 363-372
MSC (1991): Primary 65C10; Secondary 11K45
MathSciNet review: 1377661
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Abstract: 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

Keywords: Uniform pseudorandom numbers, compound nonlinear congruential method, equidistribution of subsequences, average behavior, discrepancy, incomplete exponential sums
Received by editor(s): July 13, 1995
Article copyright: © Copyright 1997 American Mathematical Society