Expanding the applicability of two-point Newton-like methods under generalized conditions

Ioannis K. Argyros, and Saïd Hilout. "Expanding the applicability of two-point Newton-like methods under generalized conditions." Applicationes Mathematicae 40.1 (2013): 63-90. <http://eudml.org/doc/280061>.

@article{IoannisK2013,
abstract = {We use a two-point Newton-like method to approximate a locally unique solution of a nonlinear equation containing a non-differentiable term in a Banach space setting. Using more precise majorizing sequences than in earlier studies, we present a tighter semi-local and local convergence analysis and weaker convergence criteria. This way we expand the applicability of these methods. Numerical examples are provided where the old convergence criteria do not hold but the new convergence criteria are satisfied.},
author = {Ioannis K. Argyros, Saïd Hilout},
journal = {Applicationes Mathematicae},
keywords = {nonlinear operator equation; Newton-like method; convergence; single-step method; numerical example},
language = {eng},
number = {1},
pages = {63-90},
title = {Expanding the applicability of two-point Newton-like methods under generalized conditions},
url = {http://eudml.org/doc/280061},
volume = {40},
year = {2013},
}

TY - JOUR
AU - Ioannis K. Argyros
AU - Saïd Hilout
TI - Expanding the applicability of two-point Newton-like methods under generalized conditions
JO - Applicationes Mathematicae
PY - 2013
VL - 40
IS - 1
SP - 63
EP - 90
AB - We use a two-point Newton-like method to approximate a locally unique solution of a nonlinear equation containing a non-differentiable term in a Banach space setting. Using more precise majorizing sequences than in earlier studies, we present a tighter semi-local and local convergence analysis and weaker convergence criteria. This way we expand the applicability of these methods. Numerical examples are provided where the old convergence criteria do not hold but the new convergence criteria are satisfied.
LA - eng
KW - nonlinear operator equation; Newton-like method; convergence; single-step method; numerical example
UR - http://eudml.org/doc/280061
ER -