A unifying convergence analysis of Newton's method for twice Fréchet-differentiable operators

I. K. Argyros, and D. González. "A unifying convergence analysis of Newton's method for twice Fréchet-differentiable operators." Applicationes Mathematicae 42.1 (2015): 29-56. <http://eudml.org/doc/279932>.

@article{I2015,
abstract = {We provide a local as well as a semilocal convergence analysis for Newton's method using unifying hypotheses on twice Fréchet-differentiable operators in a Banach space setting. Our approach extends the applicability of Newton's method. Numerical examples are also provided.},
author = {I. K. Argyros, D. González},
journal = {Applicationes Mathematicae},
keywords = {Newton method; majorizing sequence; Fréchet differentiable operator; local and semilocal convergence; Hammerstein integral equation; nonlinear operator equation; Kantorovich majorant method; numerical example},
language = {eng},
number = {1},
pages = {29-56},
title = {A unifying convergence analysis of Newton's method for twice Fréchet-differentiable operators},
url = {http://eudml.org/doc/279932},
volume = {42},
year = {2015},
}

TY - JOUR
AU - I. K. Argyros
AU - D. González
TI - A unifying convergence analysis of Newton's method for twice Fréchet-differentiable operators
JO - Applicationes Mathematicae
PY - 2015
VL - 42
IS - 1
SP - 29
EP - 56
AB - We provide a local as well as a semilocal convergence analysis for Newton's method using unifying hypotheses on twice Fréchet-differentiable operators in a Banach space setting. Our approach extends the applicability of Newton's method. Numerical examples are also provided.
LA - eng
KW - Newton method; majorizing sequence; Fréchet differentiable operator; local and semilocal convergence; Hammerstein integral equation; nonlinear operator equation; Kantorovich majorant method; numerical example
UR - http://eudml.org/doc/279932
ER -