On zero finding methods of higher order from data at one point
type: Item
instance of: scholarly article
title: On zero finding methods of higher order from data at one point
zbMATH Open document ID: 0675.65036
DOI: 10.1016/0885-064X(89)90005-8
author: James H. Curry
published in: Journal of Complexity
publication date: 1989-01-01T00:00:00Z
review text: The author generalizes to higher order methods the approach of \textit{S. Smale} [The merging of disciplines in pure, applied and computational mathematics 185-196 (1986; Zbl 0613.65058)] for the convergence analysis of iterative methods for analytic functions based on data at one point. A particular aim is here to avoid the need for schlicht-function assumptions. Two examples of cubically convergent methods are given one of which is Halley's method.
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 4106137
zbMATH Keywords: zero finding
zbMATH Keywords: higher order convergence
zbMATH Keywords: iterative methods
zbMATH Keywords: analytic functions
zbMATH Keywords: schlicht-function
zbMATH Keywords: Halley's method
reviewed by: Werner C. Rheinboldt
MaRDI profile type: Publication
cites work: Konstruktion und Durchführung von Iterationsverfahren höherer Ordnung
cites work: Q4060241
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cites work: The fundamental theorem of algebra and complexity theory
cites work: On the efficiency of algorithms of analysis
description: scientific article; zbMATH DE number 4106137