Improved ball convergence of Newton's method under general conditions

Ioannis K. Argyros, and Hongmin Ren. "Improved ball convergence of Newton's method under general conditions." Applicationes Mathematicae 39.3 (2012): 365-375. <http://eudml.org/doc/280037>.

@article{IoannisK2012,
abstract = {We present ball convergence results for Newton's method in order to approximate a locally unique solution of a nonlinear operator equation in a Banach space setting. Our hypotheses involve very general majorants on the Fréchet derivatives of the operators involved. In the special case of convex majorants our results, compared with earlier ones, have at least as large radius of convergence, no less tight error bounds on the distances involved, and no less precise information on the uniqueness of the solution.},
author = {Ioannis K. Argyros, Hongmin Ren},
journal = {Applicationes Mathematicae},
keywords = {Newton's method; Banach space; ball convergence; radius of convergence; convex majorants; nonlinear operator equation; error bounds; Fréchet derivative},
language = {eng},
number = {3},
pages = {365-375},
title = {Improved ball convergence of Newton's method under general conditions},
url = {http://eudml.org/doc/280037},
volume = {39},
year = {2012},
}

TY - JOUR
AU - Ioannis K. Argyros
AU - Hongmin Ren
TI - Improved ball convergence of Newton's method under general conditions
JO - Applicationes Mathematicae
PY - 2012
VL - 39
IS - 3
SP - 365
EP - 375
AB - We present ball convergence results for Newton's method in order to approximate a locally unique solution of a nonlinear operator equation in a Banach space setting. Our hypotheses involve very general majorants on the Fréchet derivatives of the operators involved. In the special case of convex majorants our results, compared with earlier ones, have at least as large radius of convergence, no less tight error bounds on the distances involved, and no less precise information on the uniqueness of the solution.
LA - eng
KW - Newton's method; Banach space; ball convergence; radius of convergence; convex majorants; nonlinear operator equation; error bounds; Fréchet derivative
UR - http://eudml.org/doc/280037
ER -