Semilocal convergence analysis of convex acceleration Newton's method under majorant condition in Banach space

Shwet Nisha; P. K. Parida; A. K.  Singh

doi:10.5269/bspm.66874

Shwet Nisha Department of Mathematics, Gaya College of Engineering, Gaya-823003, India
P. K. Parida Assistant Professor Department of Mathematics Central University Jharkhana, INDIA
A. K. Singh Department of Mathematics, Cambridge Institute of Technology, Ranchi-835103, India

Abstract

This paper is devoted to give the semilocal convergence analysis of convex acceleration Newton’s method under a new type of majorant condition for solving nonlinear operator equation in Banach space. This iterative method is used for finding roots of nonlinear equations. We have used the new type of majorant condition which does not assume existence of it’s second derivative. We proposed convergence theorem which established Q-cubic convergence of the method and it’s error estimation. We have illustrated two numerical examples based on our analysis to show the efficacy of our result. Computational order of convergence for both the examples have also been given.

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Author Biographies

Shwet Nisha, Department of Mathematics, Gaya College of Engineering, Gaya-823003, India

Department of Mathematics, Gaya College of Engineering, Gaya-823003, India

A. K. Singh, Department of Mathematics, Cambridge Institute of Technology, Ranchi-835103, India

Department of Mathematics, Cambridge Institute of Technology, Ranchi-835103, India

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