Next Article in Journal / Special Issue
Expanding the Applicability of a Third Order Newton-Type Method Free of Bilinear Operators
Previous Article in Journal / Special Issue
Local Convergence of an Optimal Eighth Order Method under Weak Conditions
Open AccessArticle

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

by 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
*
Authors to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Alicia Cordero
Algorithms 2015, 8(3), 656-668; https://doi.org/10.3390/a8030656
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)
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
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.

Show more citation formats Show less citations formats

Article Access Map

1
Only visits after 24 November 2015 are recorded.
Back to TopTop