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

Algorithms

Juan Liang¹  Xiaowu Li²  Zhinan Wu³  Mingsheng Zhang²  Lin Wang²  Feng Pan² 

[1] Department of Science, Taiyuan Institute of Technology, Taiyuan 030008, China; E-Mail:;College of Information Engineering, Guizhou Minzu University, Guiyang 550025, China;School of Mathematics and Computer Science, Yichun University, Yichun 336000, China; E-Mail:

关键词: nonlinear equation;    multiple roots;    newton-like method;    high-order convergence;    iterative methods;   

DOI  :  10.3390/a8030656

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.