Machine iteration of a linear function: Local behaviour
type: Item
instance of: scholarly article
title: Machine iteration of a linear function: Local behaviour
zbMATH Open document ID: 0726.65046
DOI: 10.1016/0898-1221(91)90091-H
author: P. M. Binder
publication date: 1991-01-01T00:00:00Z
review text: The paper deals with a computer which represents numbers as multiples of a discretization step \(\delta\). For floating-point representation, this means that all numbers should be of the same order of magnitude. The local behaviour of the linear function \(f(x)=ax+(1-a)\zeta\) is studied near its fixed point \(\zeta\). In the case of truncation, the author calculates the conditions needed for spurious multiple fixed points and for period-two cycles. Neither of these two errors can be reduced with better machine precision. Important qualitative differences between the schemes of roundoff and truncation are also shown.
Mathematics Subject Classification ID: 65G50
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 4199479
zbMATH Keywords: machine linear iteration
zbMATH Keywords: truncation
zbMATH Keywords: spurious multiple fixed points
zbMATH Keywords: period-two cycles
zbMATH Keywords: roundoff
reviewed by: S. M. Grzegórski
MaRDI profile type: Publication
cites work: Effects of phase space discretization on the long-time behavior of dynamical systems
full work available at URL: 0898-1221(91)90091-h
OpenAlex ID: W2020351135
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4199479