A UNIFYING SEMI-LOCAL ANALYSIS FOR ITERATIVE ALGORITHMS OF HIGH CONVERGENCE ORDER

Authors

  • IOANNIS K. ARGYROS Department of Mathematical Sciences, Cameron University, Lawton, Oklahoma 73505-6377, USA
  • S.K. KHATTRI Department of Engineering, Stord Haugesund University College, Norway

Keywords:

Two-point Newton type methods, Banach space, majorizing sequence, semilocal convergence, recurrent functions

Abstract

We present a unifying semi-local convergence analysis of two-step Newton-type methods for solving nonlinear equations in a Banach space setting. Convergence order of these methods is higher than two. Our analysis expands the applicability of these methods by providing weaker convergence criteria and a convergence analysis-which is tighter than earlier studies [see 1-4,24-34] - is also presented. Numerical examples illustrating the developed theoretical results are also given.

Additional Files

Published

07/07/2013

Issue

Vol. 4 No. 2 (2013): JNAO

Section

Research Articles

License

Copyright (c) 2024 Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO)

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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.