On the convergence of Newton's method under ω*-conditioned second derivative

Ioannis K. Argyros, and Saïd Hilout. "On the convergence of Newton's method under ω*-conditioned second derivative." Applicationes Mathematicae 38.3 (2011): 341-355. <http://eudml.org/doc/279862>.

@article{IoannisK2011,
abstract = {We provide a new semilocal result for the quadratic convergence of Newton's method under ω*-conditioned second Fréchet derivative on a Banach space. This way we can handle equations where the usual Lipschitz-type conditions are not verifiable. An application involving nonlinear integral equations and two boundary value problems is provided. It turns out that a similar result using ω-conditioned hypotheses can provide usable error estimates indicating only linear convergence for Newton's method.},
author = {Ioannis K. Argyros, Saïd Hilout},
journal = {Applicationes Mathematicae},
keywords = {Newton's method; Banach space; Fréchet derivative; majorizing sequences; -conditioned derivative},
language = {eng},
number = {3},
pages = {341-355},
title = {On the convergence of Newton's method under ω*-conditioned second derivative},
url = {http://eudml.org/doc/279862},
volume = {38},
year = {2011},
}

TY - JOUR
AU - Ioannis K. Argyros
AU - Saïd Hilout
TI - On the convergence of Newton's method under ω*-conditioned second derivative
JO - Applicationes Mathematicae
PY - 2011
VL - 38
IS - 3
SP - 341
EP - 355
AB - We provide a new semilocal result for the quadratic convergence of Newton's method under ω*-conditioned second Fréchet derivative on a Banach space. This way we can handle equations where the usual Lipschitz-type conditions are not verifiable. An application involving nonlinear integral equations and two boundary value problems is provided. It turns out that a similar result using ω-conditioned hypotheses can provide usable error estimates indicating only linear convergence for Newton's method.
LA - eng
KW - Newton's method; Banach space; Fréchet derivative; majorizing sequences; -conditioned derivative
UR - http://eudml.org/doc/279862
ER -