Increasing the order of convergence for iterative methods in Banach space under weak conditions

Ioannis K. Argyros 1 and Santhosh George 2 *

doi:10.26637/MJM0602/0016

Increasing the order of convergence for iterative methods in Banach space under weak conditions

Authors :

Ioannis K. Argyros¹ and Santhosh George ^{2 *}

Author Address :

¹ Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA.
² Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka-575 025, India.

*Corresponding author.

Abstract :

We study the method considered in Xiao and Yin (2015), for solving systems of nonlinear equations, modified suitably to include the nonlinear equations in Banach spaces. The novelty of this study lies in the fact that our conditions are weaker than the conditions used in earlier studies. This way we extend the applicability of the method. Numerical examples are also given in this study where earlier results cannot apply to solve equations but our results can apply.

Keywords :

Newton-type method, radius of convergence, local convergence, restricted convergence domains.

DOI :

10.26637/MJM0602/0016

Article Info :

Received : October 02, 2017; Accepted : January 28, 2018.