Long-range correlations in linear and non-linear random number generators
type: Item
instance of: scholarly article
title: Long-range correlations in linear and non-linear random number generators
zbMATH Open document ID: 0712.65005
DOI: 10.1016/0167-8191(90)90108-L
author: A. De Matteis
author: Simonetta Pagnutti
published in: Parallel Computing
publication date: 1990-01-01T00:00:00Z
review text: This paper generalizes the authors' earlier results [Numer. Math. 53, 595-608 (1988; Zbl 0633.65006)]. Consider the sequence \(\{x_ n\}\), \(n=1,2,3,..\). \(x_{n+1}=f(x_ n)mod m\). Let the generation rule fulfil the condition that the period halves when the module m halves. Let \(L=2d\) be the period of the generator. Then the points \((x_ n,x_{n+d})\) lie in no more than two parallel lines in the square with the side m. This result shows that it is necessary to discard half of the generated sequence for almost all known generators (e.g. inversive generators).
Mathematics Subject Classification ID: 65C10
Mathematics Subject Classification ID: 11K45
zbMATH DE Number: 4172232
zbMATH Keywords: parallel computing
zbMATH Keywords: MIMD computer
zbMATH Keywords: pseudorandom numbers
zbMATH Keywords: congruential generators
zbMATH Keywords: linear and non-linear methods
zbMATH Keywords: long-range correlations
zbMATH Keywords: inversive generators
reviewed by: Jaroslav Král
MaRDI profile type: Publication
full work available at URL: 0167-8191(90)90108-l
OpenAlex ID: W2143511725
description: scientific article; zbMATH DE number 4172232