On the discrepancy of quadratic congruential pseudorandom numbers
type: Item
instance of: scholarly article
title: On the discrepancy of quadratic congruential pseudorandom numbers
zbMATH Open document ID: 0731.11046
DOI: 10.1016/0377-0427(91)90046-M
author: Harald Niederreiter
author: Jürgen Eichenauer-Herrmann
published in: Journal of Computational and Applied Mathematics
publication date: 1991-01-01T00:00:00Z
review text: Knuth's quadratic congruential method [\textit{D. E. Knuth}, The Art of Computer Programming, Vol. 2 (1981; Zbl 0477.65002)] is analysed to examine the statistical independence of consecutive pairs in the pseudorandom stream produced. The basic congruence is \[ y_{n+1}\equiv ay^ 2_ n+by_ n+c(mod p^ m)\quad (n\geq 0) \] and a,b,c are to have optimal properties. Inequality results are obtained for the appropriately described discrepancy measure and this enables a contrast to be made with the performance of the linear congruential method mod \(p^ m\).
Mathematics Subject Classification ID: 11K45
Mathematics Subject Classification ID: 65C10
zbMATH DE Number: 4208183
zbMATH Keywords: pseudorandom numbers
zbMATH Keywords: quadratic congruential method
zbMATH Keywords: statistical independence of consecutive pairs
zbMATH Keywords: discrepancy measure
reviewed by: Brian Conolly
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4208183