Constructing a family of optimal eighth-order modified Newton-type multiple-zero finders along with the dynamics behind their purely imaginary extraneous fixed points

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Authors
Geum, Young Hee
Kim, Young Ik
Neta, Beny
Subjects
Multiple-zero finder
Extraneous fixed point
Modified Newton's method
Basins of attraction
Advisors
Date of Issue
2018
Date
Publisher
Elsevier
Language
Abstract
An optimal family of eighth-order multiple-zero finders and the dynamics behind their basins of attraction are proposed by considering modified Newton-type methods with multivariate weight functions. Extensive investigation of purely imaginary extraneous fixed points of the proposed iterative methods is carried out for the study of the dynamics associated with corresponding basins of attraction. Numerical experiments strongly support the underlying theory pursued in this paper. An exploration of the relevant dynamics of the proposed methods is presented along with illustrative basins of attraction for various polynomials.
Type
Article
Description
URI
https://hdl.handle.net/10945/56408
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Research Fund of Dankook University
Funder
Format
26 p.
Citation
Y.H. Geum, Y.I. Kim, B. Neta, "Constructing a family of optimal eighth-order modified Newton-type multiple-zero finders along with the dynamics behind their purely imaginary extraneous fixed points," Journal of Computational and Applied Mathematics, v. 333, (2018), pp. 131-156.
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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.
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