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Algorithms 2015, 8(3), 656-668; doi:10.3390/a8030656

Fifth-Order Iterative Method for Solving Multiple Roots of the Highest Multiplicity of Nonlinear Equation

1,†
,
2,†,* , 3,†
,
2,†,* , 2,†,* and 2,†,*
1
Department of Science, Taiyuan Institute of Technology, Taiyuan 030008, China
2
College of Information Engineering, Guizhou Minzu University, Guiyang 550025, China
3
School of Mathematics and Computer Science, Yichun University, Yichun 336000, China
These authors contributed equally to this work.
*
Authors to whom correspondence should be addressed.
Academic Editor: Alicia Cordero
Received: 8 June 2015 / Revised: 27 July 2015 / Accepted: 14 August 2015 / Published: 20 August 2015
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
View Full-Text   |   Download PDF [306 KB, uploaded 20 August 2015]

Abstract

A three-step iterative method with fifth-order convergence as a new modification of Newton’s method was presented. This method is for finding multiple roots of nonlinear equation with unknown multiplicity m whose multiplicity m is the highest multiplicity. Its order of convergence is analyzed and proved. Results for some numerical examples show the efficiency of the new method. View Full-Text
Keywords: nonlinear equation; multiple roots; newton-like method; high-order convergence; iterative methods nonlinear equation; multiple roots; newton-like method; high-order convergence; iterative methods
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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MDPI and ACS Style

Liang, J.; Li, X.; Wu, Z.; Zhang, M.; Wang, L.; Pan, F. Fifth-Order Iterative Method for Solving Multiple Roots of the Highest Multiplicity of Nonlinear Equation. Algorithms 2015, 8, 656-668.

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