Convergence domains under Zabrejko-Zinčenko conditions using recurrent functions

Ioannis K. Argyros, and Saïd Hilout. "Convergence domains under Zabrejko-Zinčenko conditions using recurrent functions." Applicationes Mathematicae 38.2 (2011): 193-209. <http://eudml.org/doc/279884>.

@article{IoannisK2011,
abstract = {We provide a semilocal convergence analysis for Newton-type methods using our idea of recurrent functions in a Banach space setting. We use Zabrejko-Zinčenko conditions. In particular, we show that the convergence domains given before can be extended under the same computational cost. Numerical examples are also provided to show that we can solve equations in cases not covered before.},
author = {Ioannis K. Argyros, Saïd Hilout},
journal = {Applicationes Mathematicae},
keywords = {Newton-like methods; majorizing recurrent functions; nonlinear integral equations; Zabrejko-Zinçenko-type conditions; Kantorovich hypothesis; Green's kernel; nonlinear operator equation; Banach spaces; convergence; numerical example},
language = {eng},
number = {2},
pages = {193-209},
title = {Convergence domains under Zabrejko-Zinčenko conditions using recurrent functions},
url = {http://eudml.org/doc/279884},
volume = {38},
year = {2011},
}

TY - JOUR
AU - Ioannis K. Argyros
AU - Saïd Hilout
TI - Convergence domains under Zabrejko-Zinčenko conditions using recurrent functions
JO - Applicationes Mathematicae
PY - 2011
VL - 38
IS - 2
SP - 193
EP - 209
AB - We provide a semilocal convergence analysis for Newton-type methods using our idea of recurrent functions in a Banach space setting. We use Zabrejko-Zinčenko conditions. In particular, we show that the convergence domains given before can be extended under the same computational cost. Numerical examples are also provided to show that we can solve equations in cases not covered before.
LA - eng
KW - Newton-like methods; majorizing recurrent functions; nonlinear integral equations; Zabrejko-Zinçenko-type conditions; Kantorovich hypothesis; Green's kernel; nonlinear operator equation; Banach spaces; convergence; numerical example
UR - http://eudml.org/doc/279884
ER -