On the Convergence Region of Multi-step Chebyshev-Halley-type Schemes for Solving Equations

  • Ioannis K. Argyros Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
  • Santhosh George Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore 575 025, India
DOI: https://doi.org/10.34198/ejms.1219.187207
Keywords: Chebyshev method, Halley method, local convergence, semi-local convergence, Fréchet derivative, ω-conditions

Abstract

The aim of this article is to extend the convergence region of certain multi-step Chebyshev-Halley-type schemes for solving Banach space valued nonlinear equations. In particular, we find an at least as small region as the region of the operator involved containing the iterates. This way the majorant functions are tighter than the ones related to the original region, leading to a finer local as well as a semi-local convergence analysis under the same computational effort. Numerical examples complete this article.

Published
2019-03-19
How to Cite
Argyros, I. K., & George, S. (2019). On the Convergence Region of Multi-step Chebyshev-Halley-type Schemes for Solving Equations . Earthline Journal of Mathematical Sciences, 1(2), 187-207. https://doi.org/10.34198/ejms.1219.187207
Issue
Vol 1 No 2 (2019)
Section
Articles


This work is licensed under a Creative Commons Attribution 4.0 International License.