A semilocal convergence analysis for directional Newton methods

Argyros, Ioannis

doi:10.1090/S0025-5718-2010-02398-1

A semilocal convergence analysis for directional Newton methods
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by Ioannis K. Argyros;

Math. Comp. 80 (2011), 327-343

DOI: https://doi.org/10.1090/S0025-5718-2010-02398-1

Published electronically: July 8, 2010

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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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