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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On the distribution of inversive congruential pseudorandom numbers in parts of the period


Authors: Harald Niederreiter and Igor E. Shparlinski
Journal: Math. Comp. 70 (2001), 1569-1574
MSC (2000): Primary 11K45, 65C10; Secondary 11K38, 11L07, 11T23
Published electronically: June 12, 2000
MathSciNet review: 1836919
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Abstract:

The inversive congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. In this paper we present the first nontrivial bounds on the discrepancy of individual sequences of inversive congruential pseudorandom numbers in parts of the period. The proof is based on a new bound for certain incomplete exponential sums.


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Additional Information

Harald Niederreiter
Affiliation: Institute of Discrete Mathematics, Austrian Academy of Sciences, Sonnenfelsgasse 19, A–1010 Vienna, Austria
Email: niederreiter@oeaw.ac.at

Igor E. Shparlinski
Affiliation: Department of Computing, Macquarie University, New South Wales 2109, Australia
Email: igor@comp.mq.edu.au

DOI: http://dx.doi.org/10.1090/S0025-5718-00-01273-4
PII: S 0025-5718(00)01273-4
Keywords: Pseudorandom numbers, inversive congruential method, discrepancy, exponential sums
Received by editor(s): November 17, 1998
Received by editor(s) in revised form: November 19, 1999
Published electronically: June 12, 2000
Article copyright: © Copyright 2000 American Mathematical Society