Local convergence for some third-order iterative methods under weak conditions

Ioannis K. Argyros; Yeol Je Cho; Santhosh George

doi:10.4134/JKMS.j150244

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

QR
Code

Article

HOME

ALL ARTICLES

View

J. Korean Math. Soc. 2016; 53(4): 781-793

Printed July 1, 2016

https://doi.org/10.4134/JKMS.j150244

Local convergence for some third-order iterative methods under weak conditions

Ioannis K. Argyros, Yeol Je Cho, and Santhosh George

Cameron University, King Abdulaziz University, Department of Mathematical and Computational Sciences

Abstract

Go to

Abstract

The solutions of equations are usually found using iterative methods whose convergence order is determined by Taylor expansions. In particular, the local convergence of the method we study in this paper is shown under hypotheses reaching the third derivative of the operator involved. These hypotheses limit the applicability of the method. In our study we show convergence of the method using only the first derivative. This way we expand the applicability of the method. Numerical examples show the applicability of our results in cases earlier results cannot.

Keywords: Newton method, order of convergence, local convergence

MSC numbers: 65D10, 65D99