Ostrowski-Kantorovich theorem of Halley method for solving nonlinear operator equations in Banach spaces is presented. The complete expression of an upper bound for the method is given based on the initial information. Also some properties of $S$-order of convergence and sufficient asymptotic error bound will be discussed.
@article{118565,
author = {Dong Chen},
title = {Ostrowski-Kantorovich theorem and $S$-order of convergence of Halley method in Banach spaces},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {34},
year = {1993},
pages = {153-163},
zbl = {0786.65051},
mrnumber = {1240213},
language = {en},
url = {http://dml.mathdoc.fr/item/118565}
}
Chen, Dong. Ostrowski-Kantorovich theorem and $S$-order of convergence of Halley method in Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 153-163. http://gdmltest.u-ga.fr/item/118565/
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