A new Kantorovich-type convergence theorem for Newton's method is established for approximating a locally unique solution of an equation F(x)=0 defined on a Banach space. It is assumed that the operator F is twice Fréchet differentiable, and that F', F'' satisfy Lipschitz conditions. Our convergence condition differs from earlier ones and therefore it has theoretical and practical value.
@article{bwmeta1.element.bwnjournal-article-zmv26i2p151bwm,
author = {Ioannis Argyros},
title = {A new Kantorovich-type theorem for Newton's method},
journal = {Applicationes Mathematicae},
volume = {26},
year = {1999},
pages = {151-157},
zbl = {0998.65059},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv26i2p151bwm}
}
Argyros, Ioannis. A new Kantorovich-type theorem for Newton's method. Applicationes Mathematicae, Tome 26 (1999) pp. 151-157. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv26i2p151bwm/
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