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

    Authors

    • Samundra Regmi 1
    • Ioannis Konstantinos Argyros 2
    • Santhosh George 3
    • Christopher I. Argyros 4

    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

10.52547/CMCMA.1.1.63
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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

  • semi-local convergence
  • Homeier method
  • iterative methods
  • Banach space
  • convergence criterion
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Computational Mathematics and Computer Modeling with Applications (CMCMA)
Volume 1, Issue 1 - Serial Number 1
June 2022
Pages 63-68
Files
  • XML
  • PDF 222.33 K
History
  • Receive Date: 15 February 2022
  • Accept Date: 18 March 2022
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How to cite
  • RIS
  • EndNote
  • Mendeley
  • BibTeX
  • APA
  • MLA
  • HARVARD
  • CHICAGO
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Statistics
  • Article View: 501
  • PDF Download: 259

APA

Regmi, S. , Argyros, I. K. , George, S. and Argyros, C. I. (2022). On the semi-local convergence of the Homeier method in Banach space for solving equations. Computational Mathematics and Computer Modeling with Applications (CMCMA), 1(1), 63-68. doi: 10.52547/CMCMA.1.1.63

MLA

Regmi, S. , , Argyros, I. K. , , George, S. , and Argyros, C. I.. "On the semi-local convergence of the Homeier method in Banach space for solving equations", Computational Mathematics and Computer Modeling with Applications (CMCMA), 1, 1, 2022, 63-68. doi: 10.52547/CMCMA.1.1.63

HARVARD

Regmi, S., Argyros, I. K., George, S., Argyros, C. I. (2022). 'On the semi-local convergence of the Homeier method in Banach space for solving equations', Computational Mathematics and Computer Modeling with Applications (CMCMA), 1(1), pp. 63-68. doi: 10.52547/CMCMA.1.1.63

CHICAGO

S. Regmi , I. K. Argyros , S. George and C. I. Argyros, "On the semi-local convergence of the Homeier method in Banach space for solving equations," Computational Mathematics and Computer Modeling with Applications (CMCMA), 1 1 (2022): 63-68, doi: 10.52547/CMCMA.1.1.63

VANCOUVER

Regmi, S., Argyros, I. K., George, S., Argyros, C. I. On the semi-local convergence of the Homeier method in Banach space for solving equations. Computational Mathematics and Computer Modeling with Applications (CMCMA), 2022; 1(1): 63-68. doi: 10.52547/CMCMA.1.1.63

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