On optimal parameter of Laguerre’s family of zero-finding methods
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Authors
Petković, L.D.
Petković, M.S.
Neta, B.
Subjects
nonlinear equations
dynamic study
basin of attraction
convergence behaviour
dynamic study
basin of attraction
convergence behaviour
Advisors
Date of Issue
2017-12-24
Date
24 December 2017
Publisher
Taylor & Francis
Language
Abstract
A one parameter Laguerre's family of iterative methods for solving nonlinear
equations is considered. This family includes the Halley, Ostrowski and
Euler methods, most frequently used one-point third-order methods for
finding zeros. Investigation of convergence quality of these methods and
their ranking is reduced to searching optimal parameter of Laguerre’s family,
which is the main goal of this paper. Although methods from Laguerre’s
family have been extensively studied in the literature for more decades,
their proper ranking was primarily discussed according to numerical experiments.
Regarding that such ranking is not trustworthy even for algebraic
polynomials, more reliable comparison study is presented by combining
the comparison by numerical examples and the comparison using dynamic
study of methods by basins of attraction that enable their graphic visualization.
This combined approach has shown that Ostrowski’s method
possesses the best convergence behaviour for most polynomial equations.
Type
Article
Description
The article of record as published may be found at http://doi.org/10.1080/00207160.2018.1429598
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Serbian Ministry of Education and Science
Funder
Grant 174022
Format
16 p.
Citation
L.D. Petković, M.S. Petković and B. Neta "On optimal parameter of Laguerre’s family of zero-finding methods," International Journal of Computer Mathematics, pages 1-16, Received 25 Apr 2017, Accepted 24 Dec 2017, Accepted author version posted online: 19 Jan 2018 Published online: 04 February 2018.
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.