On the convergence of two-step Newton-type methods of high efficiency index

Ioannis K. Argyros, and Saïd Hilout. "On the convergence of two-step Newton-type methods of high efficiency index." Applicationes Mathematicae 36.4 (2009): 465-499. <http://eudml.org/doc/280077>.

@article{IoannisK2009,
abstract = {We introduce a new idea of recurrent functions to provide a new semilocal convergence analysis for two-step Newton-type methods of high efficiency index. It turns out that our sufficient convergence conditions are weaker, and the error bounds are tighter than in earlier studies in many interesting cases. Applications and numerical examples, involving a nonlinear integral equation of Chandrasekhar type, and a differential equation containing a Green's kernel are also provided.},
author = {Ioannis K. Argyros, Saïd Hilout},
journal = {Applicationes Mathematicae},
keywords = {two-step Newton-type method; semilocal convergence; Banach space; differential equation of Hammerstein type; nonlinear operator-equation; Fréchet-differentiable operator; numerical examples},
language = {eng},
number = {4},
pages = {465-499},
title = {On the convergence of two-step Newton-type methods of high efficiency index},
url = {http://eudml.org/doc/280077},
volume = {36},
year = {2009},
}

TY - JOUR
AU - Ioannis K. Argyros
AU - Saïd Hilout
TI - On the convergence of two-step Newton-type methods of high efficiency index
JO - Applicationes Mathematicae
PY - 2009
VL - 36
IS - 4
SP - 465
EP - 499
AB - We introduce a new idea of recurrent functions to provide a new semilocal convergence analysis for two-step Newton-type methods of high efficiency index. It turns out that our sufficient convergence conditions are weaker, and the error bounds are tighter than in earlier studies in many interesting cases. Applications and numerical examples, involving a nonlinear integral equation of Chandrasekhar type, and a differential equation containing a Green's kernel are also provided.
LA - eng
KW - two-step Newton-type method; semilocal convergence; Banach space; differential equation of Hammerstein type; nonlinear operator-equation; Fréchet-differentiable operator; numerical examples
UR - http://eudml.org/doc/280077
ER -