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On the semi-local convergence of the Homeier method in Banach space for solving equations

    Authors

    1 Learning Commons, University of North Texas at Dallas, Dallas, TX, USA

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

    3 Department of Mathematical and Computational Sciences,National Institute of Technology Karnataka, India-575 025

    4 Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA

,

Document Type : Invited paper

Abstract

In this paper we consider the semi-local convergence analysis of the Homeier method for solving nonlinear equation in Banach space. As far as we know no semi-local convergence has been given for the Homeier under Lipschitz conditions. Our goal is to extend the applicability of the Homeier method in the semi-local convergence under these conditions. We use majorizing sequences and conditions only on the first derivative which appear on the method for proving our results. Numerical experiments are provided in this study.

Keywords

Computational Mathematics and Computer Modeling with Applications (CMCMA)
Volume 1, Issue 1 - Serial Number 1
June 2022
Pages 63-68
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History
  • Receive Date: 15 February 2022
  • Accept Date: 18 March 2022
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