New unifying convergence criteria for Newton-like methods

Ioannis K. Argyros. "New unifying convergence criteria for Newton-like methods." Applicationes Mathematicae 29.3 (2002): 359-369. <http://eudml.org/doc/279246>.

@article{IoannisK2002,
abstract = {We present a local and a semilocal analysis for Newton-like methods in a Banach space. Our hypotheses on the operators involved are very general. It turns out that by choosing special cases for the "majorizing" functions we obtain all previous results in the literature, but not vice versa. Since our results give a deeper insight into the structure of the functions involved, we can obtain semilocal convergence under weaker conditions and in the case of local convergence a larger convergence radius.},
author = {Ioannis K. Argyros},
journal = {Applicationes Mathematicae},
keywords = {Banach space; Newton-like method; Fréchet derivative; majorizing sequence; non-differentiable operator; semilocal convergence},
language = {eng},
number = {3},
pages = {359-369},
title = {New unifying convergence criteria for Newton-like methods},
url = {http://eudml.org/doc/279246},
volume = {29},
year = {2002},
}

TY - JOUR
AU - Ioannis K. Argyros
TI - New unifying convergence criteria for Newton-like methods
JO - Applicationes Mathematicae
PY - 2002
VL - 29
IS - 3
SP - 359
EP - 369
AB - We present a local and a semilocal analysis for Newton-like methods in a Banach space. Our hypotheses on the operators involved are very general. It turns out that by choosing special cases for the "majorizing" functions we obtain all previous results in the literature, but not vice versa. Since our results give a deeper insight into the structure of the functions involved, we can obtain semilocal convergence under weaker conditions and in the case of local convergence a larger convergence radius.
LA - eng
KW - Banach space; Newton-like method; Fréchet derivative; majorizing sequence; non-differentiable operator; semilocal convergence
UR - http://eudml.org/doc/279246
ER -