Extended Local Convergence for the Chebyshev Method under the Majorant Condition
Ioannis K. Argyros
Department of Computing and Mathematical Sciences, Cameron University, Lawton, 73505, OK, USA.
Jinny Ann John
Department of Mathematics, Puducherry Technological University, Pondicherry-605014, India.
Jayakumar Jayaraman *
Department of Mathematics, Puducherry Technological University, Pondicherry-605014, India.
Samundra Regmi
Department of Mathematics, University of Houston, Houston, TX, 77204, USA.
*Author to whom correspondence should be addressed.
Abstract
In this article, we present the study on local convergence behaviour of Chebyshev's method, which is a third order iterative method used to solve a non-linear system in Banach space locale. In contrast to the earlier works, we establish the convergence using restricted-majorant conditions. As a result, we get better
convergence radius and more tighter error estimates in comparison to the previous researches. Suitable numerical examples complement the theory.
Keywords: Non-linear equations, Fréchet derivative, local convergence, banach space