Local convergence theorems for Newton's method from data at one point

Ioannis K. Argyros. "Local convergence theorems for Newton's method from data at one point." Applicationes Mathematicae 29.4 (2002): 481-486. <http://eudml.org/doc/279298>.

@article{IoannisK2002,
abstract = {We provide local convergence theorems for the convergence of Newton's method to a solution of an equation in a Banach space utilizing only information at one point. It turns out that for analytic operators the convergence radius for Newton's method is enlarged compared with earlier results. A numerical example is also provided that compares our results favorably with earlier ones.},
author = {Ioannis K. Argyros},
journal = {Applicationes Mathematicae},
keywords = {Banach space; Newton's method; Fréchet-differentiable/analytic operator; convergence; nonlinear operator equation; numerical example},
language = {eng},
number = {4},
pages = {481-486},
title = {Local convergence theorems for Newton's method from data at one point},
url = {http://eudml.org/doc/279298},
volume = {29},
year = {2002},
}

TY - JOUR
AU - Ioannis K. Argyros
TI - Local convergence theorems for Newton's method from data at one point
JO - Applicationes Mathematicae
PY - 2002
VL - 29
IS - 4
SP - 481
EP - 486
AB - We provide local convergence theorems for the convergence of Newton's method to a solution of an equation in a Banach space utilizing only information at one point. It turns out that for analytic operators the convergence radius for Newton's method is enlarged compared with earlier results. A numerical example is also provided that compares our results favorably with earlier ones.
LA - eng
KW - Banach space; Newton's method; Fréchet-differentiable/analytic operator; convergence; nonlinear operator equation; numerical example
UR - http://eudml.org/doc/279298
ER -