We provide new local and semilocal convergence results for Newton's method. We introduce Lipschitz-type hypotheses on the mth-Frechet derivative. This way we manage to enlarge the radius of convergence of Newton's method. Numerical examples are also provided to show that our results guarantee convergence where others do not.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am28-1-1,
author = {Ioannis K. Argyros},
title = {On a new method for enlarging the radius of convergence for Newton's method},
journal = {Applicationes Mathematicae},
volume = {28},
year = {2001},
pages = {1-15},
zbl = {1008.65033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-1-1}
}
Ioannis K. Argyros. On a new method for enlarging the radius of convergence for Newton's method. Applicationes Mathematicae, Tome 28 (2001) pp. 1-15. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-1-1/