On the average distribution of inversive pseudorandom numbers
type: Item
instance of: scholarly article
title: On the average distribution of inversive pseudorandom numbers
zbMATH Open document ID: 1027.11054
author: Igor E. Shparlinski
author: Harald Niederreiter
published in: Finite Fields and their Applications
publication date: 2003-04-02T00:00:00Z
review text: Nonlinear methods are attractive alternatives to linear methods for pseudorandom number generation. In particular the inversive methods have many desirable features [see e.g. the author's survey, Recent advances in the theory of nonlinear pseudorandom number generators. Proc. Conf. Monte Carlo and quasi-Monte Carlo methods 2000, Hong Kong, Berlin: Springer, 86--102 (2002; Zbl 1076.65008)]. Here the behaviour of inversive pseudorandom numbers on average over all initial values is investigated. The results are much stronger than for the worst case [see \textit{J. Gutierrez} and the authors, Monatsh. Math. 129, 31--36 (2000; Zbl 1011.11053) and the authors, Appl. Algebra Eng. Commun. Comput. 10, 189--202 (2000; Zbl 0999.11040)]. For different average case results over all inversive sequences obtained by multiplying a fixed sequence with a nonzero constant see \textit{J. Eichenauer-Herrmann} and \textit{F. Emmerich} [Math. Comput. 65, 215--225 (1996; Zbl 0852.11041)] and \textit{F. Emmerich} [Math. Comput. 71, 781--791 (2002; Zbl 0991.65004)].
reviewed by: Arne Winterhof
Mathematics Subject Classification ID: 11K45
Mathematics Subject Classification ID: 11K38
Mathematics Subject Classification ID: 65C10
Mathematics Subject Classification ID: 11L07
Mathematics Subject Classification ID: 11T23
zbMATH DE Number: 1891461
zbMATH Keywords: inversive pseudorandom numbers
zbMATH Keywords: discrepancy
zbMATH Keywords: average case analysis
zbMATH Keywords: incomplete exponential sums
MaRDI profile type: Publication
full work available at URL: ffta.2002.0358
OpenAlex ID: W1977292688
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DOI: 10.1006/FFTA.2002.0358
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description: scientific article; zbMATH DE number 1891461