On the distribution of pseudorandom numbers and vectors generated by inversive methods
type: Item
instance of: scholarly article
title: On the distribution of pseudorandom numbers and vectors generated by inversive methods
zbMATH Open document ID: 0999.11040
author: Igor E. Shparlinski
author: Harald Niederreiter
published in: Applicable Algebra in Engineering, Communication and Computing
publication date: 2001-10-23T00:00:00Z
review text: Inversive methods are attractive alternatives to linear methods for pseudorandom number generation. A particular attractive method is the digital inversive method introduced by \textit{J. Eichenauer-Herrmann} and \textit{H. Niederreiter} [ACM Trans. Model. Comput. Simul. 4, 339-349 (1994; Zbl 0847.11038)]. Extending their method in [Math. Comput. 70, 1569-1574 (2001; Zbl 0983.11048)] the authors prove bounds on the discrepancy of sequences of digital inversive pseudorandom numbers and inversive pseudorandom vectors in parts of the period. The proofs are based on a new bound for certain exponential sums. Similar results were obtained on the digital explicit inversive method in \textit{H. Niederreiter} and \textit{A. Winterhof} [Acta Arith. 93, 387-399 (2000; Zbl 0969.11040)] and \textit{M. B. Levin} [Math. Slovaca 50, 581-598 (2000; Zbl 0990.65005)], the compound inversive method in \textit{H. Niederreiter} and \textit{A. Winterhof} [Monatsh. Math. 132, 35-48 (2001; Zbl 0983.11047)], and the inversive congruential method with odd prime power modulus in \textit{H. Niederreiter} and \textit{I. E. Shparlinski} [Acta Arith. 92, 89-98 (2000; Zbl 0949.11036)]. For a recent survey paper on this topic see \textit{H. Niederreiter} and \textit{I. E. Shparlinski} [Fang, Kai-Tai (ed.) et al., Monte Carlo and quasi-Monte Carlo methods 2000. Proceedings of a conference, Hong Kong Baptist Univ., Hong Kong SAR, China, 2000. Berlin, Springer, 86-102 (2002; Zbl 1076.65008)].
reviewed by: Arne Winterhof
Mathematics Subject Classification ID: 11K45
Mathematics Subject Classification ID: 65C10
Mathematics Subject Classification ID: 11L07
Mathematics Subject Classification ID: 11T23
Mathematics Subject Classification ID: 11K38
zbMATH DE Number: 1441260
zbMATH Keywords: digital inversive pseudorandom numbers
zbMATH Keywords: inversive pseudorandom vectors
zbMATH Keywords: discrepancy
zbMATH Keywords: exponential sums
MaRDI profile type: Publication
full work available at URL: s002000050124
OpenAlex ID: W2041874603
DOI: 10.1007/S002000050124
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description: scientific article; zbMATH DE number 1441260