The paper develops semilocal convergence of Inexact Newton Method INM for approximating solutions of nonlinear equations in Banach space setting. We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis. The results obtained compare favorably with earlier ones in at least the case of Newton's Method (NM). Numerical examples, where our convergence criteria are satisfied but the earlier ones are not, are also explored.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am40-2-6,
author = {I. K. Argyros and S. K. Khattri},
title = {Inexact Newton method under weak and center-weak Lipschitz conditions},
journal = {Applicationes Mathematicae},
volume = {40},
year = {2013},
pages = {237-258},
zbl = {1277.65039},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am40-2-6}
}
I. K. Argyros; S. K. Khattri. Inexact Newton method under weak and center-weak Lipschitz conditions. Applicationes Mathematicae, Tome 40 (2013) pp. 237-258. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am40-2-6/