We provide local convergence theorems for the convergence of Newton's method to a solution of an equation in a Banach space utilizing only information at one point. It turns out that for analytic operators the convergence radius for Newton's method is enlarged compared with earlier results. A numerical example is also provided that compares our results favorably with earlier ones.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am29-4-7,
author = {Ioannis K. Argyros},
title = {Local convergence theorems for Newton's method from data at one point},
journal = {Applicationes Mathematicae},
volume = {29},
year = {2002},
pages = {481-486},
zbl = {1009.65033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am29-4-7}
}
Ioannis K. Argyros. Local convergence theorems for Newton's method from data at one point. Applicationes Mathematicae, Tome 29 (2002) pp. 481-486. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am29-4-7/