Discrepancy bounds for nonoverlapping pairs of quadratic congruential pseudorandom numbers
type: Item
instance of: scholarly article
title: Discrepancy bounds for nonoverlapping pairs of quadratic congruential pseudorandom numbers
zbMATH Open document ID: 0832.11028
DOI: 10.1007/BF01195549
author: Jürgen Eichenauer-Herrmann
published in: Archiv der Mathematik
publication date: 1996-03-07T00:00:00Z
review text: In this paper the quadratic congruential generator is investigated: \[ y_{n+1} \equiv ay^2_n+ by_n+ c\pmod m, \qquad n\geq 0, \] where \(a\), \(b\), \(c\), \(y_0\) are given parameters in \(\mathbb{Z}_m\). Setting \(x_n= {1\over m} y_n\) one produces a quasi-random sequence in \([0,1)\), provided that the parameters are suitably chosen. The author considers pairs \({\mathbf x}_n= (x_{2n}, x_{2n+1})\) of subsequent elements and proves bounds for the two-dimensional discrepancy \(D_{m/2} ({\mathbf x}_n)\). This continues earlier investigations of H. Niederreiter and the author.
Mathematics Subject Classification ID: 11K45
Mathematics Subject Classification ID: 65C10
zbMATH DE Number: 815702
zbMATH Keywords: random number generators
zbMATH Keywords: quadratic congruential generator
zbMATH Keywords: bounds for the two-dimensional discrepancy
reviewed by: Robert F. Tichy
MaRDI profile type: Publication
cites work: On the structure of quadratic congruential sequences
cites work: A remark on the discrepancy of quadratic congruential pseudorandom numbers
cites work: Inversive Congruential Pseudorandom Numbers: A Tutorial
cites work: Q4295075
cites work: On the discrepancy of quadratic congruential pseudorandom numbers with power of two modulus
cites work: Pseudorandom Number Generation by Nonlinear Methods
cites work: On the discrepancy of quadratic congruential pseudorandom numbers
cites work: On large deviations of the empiric D.F. of vector chance variables and a law of the iterated logarithm
cites work: Q3935355
cites work: The Serial Test for Congruential Pseudorandom Numbers Generated by Inversions
cites work: Recent trends in random number and random vector generation
cites work: Q4026983
cites work: Q3136968
cites work: Q4003879
cites work: Q4295076
full work available at URL: https://doi.org/10.1007/bf01195549
OpenAlex ID: W2104767393
description: scientific article; zbMATH DE number 815702