Average errors for zero finding: Lower bounds for smooth or monotone functions
type: Item
instance of: scholarly article
title: Average errors for zero finding: Lower bounds for smooth or monotone functions
zbMATH Open document ID: 0809.65044
DOI: 10.1007/BF01832985
author: Klaus Ritter
published in: Aequationes Mathematicae
publication date: 1994-12-07T00:00:00Z
full work available at URL: https://eudml.org/doc/137607
review text: An error analysis of zero finding for monotone or \(C^ r(0; I)\) functions is presented. The errors for methods using \(n\) function or derivative evaluations are defined with respect to \(r\)-fold Wiener or Ulam measures and are understood in the root or residual sense. The author shows that it is impossible to obtain superlinear convergence even for classes of smooth functions which have only simple zeros. Besides new results, the article presents a good introduction to the problem.
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 65G50
zbMATH DE Number: 699777
zbMATH Keywords: monotone functions
zbMATH Keywords: error analysis
zbMATH Keywords: zero finding
zbMATH Keywords: superlinear convergence
zbMATH Keywords: smooth functions
reviewed by: Leonid Lebedev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 699777