J. Korean Math. Soc. 2016; 53(4): 781-793
Printed July 1, 2016
https://doi.org/10.4134/JKMS.j150244
Copyright © The Korean Mathematical Society.
Ioannis K. Argyros, Yeol Je Cho, and Santhosh George
Cameron University, King Abdulaziz University, Department of Mathematical and Computational Sciences
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
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