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A semilocal convergence analysis for directional Newton methods


Author: Ioannis K. Argyros
Journal: Math. Comp. 80 (2011), 327-343
MSC (2010): Primary 65H05, 65H10; Secondary 49M15
DOI: https://doi.org/10.1090/S0025-5718-2010-02398-1
Published electronically: July 8, 2010
MathSciNet review: 2728982
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Abstract: A semilocal convergence analysis for directional Newton methods in $ n$-variables is provided in this study. Using weaker hypotheses than in the elegant related work by Y. Levin and A. Ben-Israel and introducing the center-Lipschitz condition we provide under the same computational cost as in Levin and Ben-Israel a semilocal convergence analysis with the following advantages: weaker convergence conditions; larger convergence domain; finer error estimates on the distances involved, and an at least as precise information on the location of the zero of the function. A numerical example where our results apply to solve an equation but not the ones in Levin and Ben-Israel is also provided in this study.


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Additional Information

Ioannis K. Argyros
Affiliation: Department of Mathematics Sciences, Cameron University, Lawton, Oklahoma 73505
Email: iargyros@cameron.edu

DOI: https://doi.org/10.1090/S0025-5718-2010-02398-1
Keywords: Directional Newton method, systems of equations, Lipschitz/center-Lipschitz condition, Newton–Kantorovich-type hypothesis
Received by editor(s): May 5, 2008
Received by editor(s) in revised form: August 10, 2009
Published electronically: July 8, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.