A new class of interval methods with higher order of convergence
type: Item
instance of: scholarly article
title: A new class of interval methods with higher order of convergence
zbMATH Open document ID: 0675.65041
DOI: 10.1007/BF02243144
published in: Computing
publication date: 1989-01-01T00:00:00Z
review text: An interval iteration procedure for the inclusion of simple roots of nonlinear equations \(f(x)=0\) is described., where f is twice continuouly differentiable. Each step of the iteration procedure requires several function values and one interval evaluation of the second derivative. It is shown that if \(s\geq 5\) function values are used, then the order of convergence grows exponentially with s as \(((1+\sqrt{5})/2)^{s+1}\). Numerical experiments are reported.
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 65G30
zbMATH DE Number: 4106142
zbMATH Keywords: interval methods
zbMATH Keywords: numerical examples
zbMATH Keywords: interval iteration procedure
zbMATH Keywords: inclusion of simple roots
zbMATH Keywords: order of convergence
author: Gotz Alefeld
author: Florian A. Potra
reviewed by: Svetoslav Markov
describes a project that uses: Pascal-SC
MaRDI profile type: Publication
cites work: Q3345690
cites work: Q5723445
full work available at URL: https://doi.org/10.1007/bf02243144
OpenAlex ID: W1580082012
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description: scientific article; zbMATH DE number 4106142