Properties of interval operators
type: Item
instance of: scholarly article
title: Properties of interval operators
zbMATH Open document ID: 0589.65045
DOI: 10.1007/BF02252514
author: B. George
published in: Computing
publication date: 1986-01-01T00:00:00Z
review text: We give some properties of interval operators F which guarantee the convergence of the interval sequence \(\{X_ k\}\) defined by \(X_{k+1}:=F(X_ k)\cap X_ k\) to a unique fixed interval \(\hat X.\) This interval \(\hat X\) encloses the ''zero-set'' \(X^*\) of a function strip \(G(x):=[\underline g(x),\bar g(x)].\) For some known interval operators we investigate under which assumptions these properties are valid.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65G30
zbMATH DE Number: 3947535
zbMATH Keywords: interval iteration
zbMATH Keywords: fixed interval theorems
zbMATH Keywords: interval operators
zbMATH Keywords: convergence
MaRDI profile type: Publication
cites work: Computing Perturbation Bounds for Nonlinear Algebraic Equations
cites work: Optimal Inclusion of a Solution Set
cites work: An improved interval Newton operator
cites work: A Computational Test for Convergence of Iterative Methods for Nonlinear Systems
description: scientific article; zbMATH DE number 3947535