BALL CONVERGENCE RESULTS FOR A METHOD WITH MEMORY OF EFFICIENCY INDEX 1.8392 USING ONLY FUNCTIONAL VALUES

Authors

  • I. K. ARGYROS Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
  • S. GEORGE Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India

Keywords:

Halley’s method, local convergence, order of convergence, efficiency index

Abstract

We present a local convergence analysis for an one-step iterative method with memory of efficiency index 1.8392 to solve nonlinear equations. If the function is twice differentiable, then it was shown that the $R-$order of convergence is 1.8392. In this paper we use hypotheses up to the first derivative. This way we extend the applicability of this method. Moreover, the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented to illustrate the theoretical results.

Author Biographies

I. K. ARGYROS, Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA

Professor, Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA

S. GEORGE, Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India

Professor, Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka,

Additional Files

Published

01/19/2018

Issue

Vol. 7 No. 2 (2016): JNAO

Section

Research Articles

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Copyright (c) 2010 Journal of Nonlinear Analysis and Optimization: Theory & Applications

Creative Commons License

This work is licensed under aย Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.