The cubic semilocal convergence on two variants of Newton's method

Authors:
Quan Zheng;Rongxia Bai;Zhongli Liu
Affiliations:
College of Sciences, North China University of Technology, Beijing 100041, PR China;College of Sciences, North China University of Technology, Beijing 100041, PR China;College of Sciences, North China University of Technology, Beijing 100041, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

In this paper, we discuss two variants of Newton's method without using any second derivative for solving nonlinear equations. By using the majorant function and confirming the majorant sequences, we obtain the cubic semilocal convergence and the error estimation in the Kantorovich-type theorems. The numerical examples are presented to support the usefulness and significance.