We develop local and semilocal convergence results for Newton's method in order to solve nonlinear equations in a Banach space setting. The results compare favorably to earlier ones utilizing Lipschitz conditions on the second Fréchet derivative of the operators involved. Numerical examples where our new convergence conditions are satisfied but earlier convergence conditions are not satisfied are also reported.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am40-4-6,
author = {Ioannis K. Argyros and Sanjay K. Khattri},
title = {An improved convergence analysis of Newton's method for twice Fr\'echet differentiable operators},
journal = {Applicationes Mathematicae},
volume = {40},
year = {2013},
pages = {459-481},
zbl = {1292.65053},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am40-4-6}
}
Ioannis K. Argyros; Sanjay K. Khattri. An improved convergence analysis of Newton's method for twice Fréchet differentiable operators. Applicationes Mathematicae, Tome 40 (2013) pp. 459-481. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am40-4-6/