Expanding the Convergence Domain of Newton–like Methods and Applications in Banach Space

Authors

  • Ioannis K. Argyros Department of Mathematicsal Sciences, Cameron University, Lawton, OK 73505, USA.
  • Santhosh George Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India-757 025.

Keywords:

Newton–like method, Banach space, Lipschitz condition, convergence Domain, majorizing sequences, semilocal convergence, local convergence

Abstract

We expand the convergence domain of Newton–like methods for solving nonlinear equations in a Banach space setting. Using more precise majorizing sequences, we provide a more precise local as well as a semilocal convergence analysis than in earlier studies such as [2]- [14], [16]-[30]. Our results are illustrated by several numerical examples, for which older convergence conditions do not hold but for which our convergence conditions are satisfied.

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Published

2015-06-30

Issue

Vol. 47 No. 1 (2015)

Section

Articles

How to Cite

Expanding the Convergence Domain of Newton–like Methods and Applications in Banach Space. (2015). Punjab University Journal of Mathematics, 47(1), 1-13. https://pujm.pu.edu.pk/index.php/pujm/article/view/35