The Newton-Mysovskikh theorem provides sufficient conditions for the semilocal convergence of Newton's method to a locally unique solution of an equation in a Banach space setting. It turns out that under weaker hypotheses and a more precise error analysis than before, weaker sufficient conditions can be obtained for the local as well as semilocal convergence of Newton's method. Error bounds on the distances involved as well as a larger radius of convergence are obtained. Some numerical examples are also provided.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am33-3-9,
author = {Ioannis K. Argyros},
title = {A weaker affine covariant Newton-Mysovskikh theorem for solving equations},
journal = {Applicationes Mathematicae},
volume = {33},
year = {2006},
pages = {355-363},
zbl = {1125.65047},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am33-3-9}
}
Ioannis K. Argyros. A weaker affine covariant Newton-Mysovskikh theorem for solving equations. Applicationes Mathematicae, Tome 33 (2006) pp. 355-363. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am33-3-9/