An improved convergence analysis of Newton's method for twice Fréchet differentiable operators

Ioannis K. Argyros, and Sanjay K. Khattri. "An improved convergence analysis of Newton's method for twice Fréchet differentiable operators." Applicationes Mathematicae 40.4 (2013): 459-481. <http://eudml.org/doc/280063>.

@article{IoannisK2013,
abstract = {We develop local and semilocal convergence results for Newton's method in order to solve nonlinear equations in a Banach space setting. The results compare favorably to earlier ones utilizing Lipschitz conditions on the second Fréchet derivative of the operators involved. Numerical examples where our new convergence conditions are satisfied but earlier convergence conditions are not satisfied are also reported.},
author = {Ioannis K. Argyros, Sanjay K. Khattri},
journal = {Applicationes Mathematicae},
keywords = {Newton's method; Banach space; local convergence; semilocal convergence; Fréchet derivative; majorizing sequence},
language = {eng},
number = {4},
pages = {459-481},
title = {An improved convergence analysis of Newton's method for twice Fréchet differentiable operators},
url = {http://eudml.org/doc/280063},
volume = {40},
year = {2013},
}

TY - JOUR
AU - Ioannis K. Argyros
AU - Sanjay K. Khattri
TI - An improved convergence analysis of Newton's method for twice Fréchet differentiable operators
JO - Applicationes Mathematicae
PY - 2013
VL - 40
IS - 4
SP - 459
EP - 481
AB - We develop local and semilocal convergence results for Newton's method in order to solve nonlinear equations in a Banach space setting. The results compare favorably to earlier ones utilizing Lipschitz conditions on the second Fréchet derivative of the operators involved. Numerical examples where our new convergence conditions are satisfied but earlier convergence conditions are not satisfied are also reported.
LA - eng
KW - Newton's method; Banach space; local convergence; semilocal convergence; Fréchet derivative; majorizing sequence
UR - http://eudml.org/doc/280063
ER -