On a new method for enlarging the radius of convergence for Newton's method

Ioannis K. Argyros. "On a new method for enlarging the radius of convergence for Newton's method." Applicationes Mathematicae 28.1 (2001): 1-15. <http://eudml.org/doc/279457>.

@article{IoannisK2001,
abstract = {We provide new local and semilocal convergence results for Newton's method. We introduce Lipschitz-type hypotheses on the mth-Frechet derivative. This way we manage to enlarge the radius of convergence of Newton's method. Numerical examples are also provided to show that our results guarantee convergence where others do not.},
author = {Ioannis K. Argyros},
journal = {Applicationes Mathematicae},
keywords = {Newton's method; Banach space; radius of convergence; affine invariant operator; th Fréchet derivative; nonlinear operator equation; numerical examples},
language = {eng},
number = {1},
pages = {1-15},
title = {On a new method for enlarging the radius of convergence for Newton's method},
url = {http://eudml.org/doc/279457},
volume = {28},
year = {2001},
}

TY - JOUR
AU - Ioannis K. Argyros
TI - On a new method for enlarging the radius of convergence for Newton's method
JO - Applicationes Mathematicae
PY - 2001
VL - 28
IS - 1
SP - 1
EP - 15
AB - We provide new local and semilocal convergence results for Newton's method. We introduce Lipschitz-type hypotheses on the mth-Frechet derivative. This way we manage to enlarge the radius of convergence of Newton's method. Numerical examples are also provided to show that our results guarantee convergence where others do not.
LA - eng
KW - Newton's method; Banach space; radius of convergence; affine invariant operator; th Fréchet derivative; nonlinear operator equation; numerical examples
UR - http://eudml.org/doc/279457
ER -