On the optimality of some multi-point methods for finding multiple roots of nonlinear equation

Nonlinear Analysis

Dejan Ćebić¹  Nebojša M. Ralević¹ 

[1] University of Novi Sad, Serbia;

关键词: nonlinear equation;    multiple roots;    the modified Newton's method;    optimal order of convergence;   

DOI  :  10.15388/NA.2016.1.9

来源: DOAJ

【 摘 要 】

This paper deals with the problem of determining the multiple roots of nonlinear equations, where the multiplicity of the roots is known. The paper contains some remarks on the optimality of the recently published methods [B. Liu, X. Zhou, A new family of fourth-order methods for multiple roots of nonlinear equations, Nonlinear Anal. Model. Control, 18(2):143–152, 2013] and [X. Zhou, X. Chen, Y. Song, Families of third- and fourth-order methods for multiple roots of nonlinear equations, Appl. Math. Comput., 219(11):6030–6038, 2013]. Separate analysis of odd and even multiplicity, has shown the cases where those methods lose their optimal convergence properties. Numerical experiments are made and they support theoretical analysis.

【 授权许可】

Unknown