An optimal order method for multiple roots in case of unknown multiplicity
type: Item
instance of: scholarly article
title: An optimal order method for multiple roots in case of unknown multiplicity
zbMATH Open document ID: 1461.65077
published in: Algorithms
publication date: 2019-03-26T00:00:00Z
review text: Summary: In the literature, recently, some three-step schemes involving four function evaluations for the solution of multiple roots of nonlinear equations, whose multiplicity is not known in advance, are considered, but they do not agree with Kung-Traub's conjecture. The present article is devoted to the study of an iterative scheme for approximating multiple roots with a convergence rate of eight, when the multiplicity is hidden, which agrees with Kung-Traub's conjecture. The theoretical study of the convergence rate is investigated and demonstrated. A few nonlinear problems are presented to justify the theoretical study.
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 7042319
zbMATH Keywords: nonlinear equations
zbMATH Keywords: iterative method
zbMATH Keywords: multiple root
zbMATH Keywords: unknown multiplicity
zbMATH Keywords: optimal convergence rate
author: J. P. Jaiswal
describes a project that uses: Mathematica
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/a9010010
OpenAlex ID: W2270122196
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DOI: 10.3390/A9010010
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description: scientific article; zbMATH DE number 7042319