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Algorithms 2016, 9(1), 10; doi:10.3390/a9010010

An Optimal Order Method for Multiple Roots in Case of Unknown Multiplicity

1
Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal 462051, India
2
Faculty of Science, Barkatullah University, Bhopal, M.P. 462026, India
3
Regional Institute of Education, Bhopal, M.P. 462013, India
Academic Editors: Alicia Cordero, Juan R. Torregrosa and Francisco I. Chicharro
Received: 20 October 2015 / Revised: 7 January 2016 / Accepted: 18 January 2016 / Published: 22 January 2016
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
View Full-Text   |   Download PDF [387 KB, uploaded 22 January 2016]

Abstract

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. View Full-Text
Keywords: nonlinear equations; iterative method; multiple root; unknown multiplicity; optimal convergence rate nonlinear equations; iterative method; multiple root; unknown multiplicity; optimal convergence rate
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Jaiswal, J.P. An Optimal Order Method for Multiple Roots in Case of Unknown Multiplicity. Algorithms 2016, 9, 10.

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