A weaker affine covariant Newton-Mysovskikh theorem for solving equations

Ioannis K. Argyros. "A weaker affine covariant Newton-Mysovskikh theorem for solving equations." Applicationes Mathematicae 33.3-4 (2006): 355-363. <http://eudml.org/doc/279402>.

@article{IoannisK2006,
abstract = {The Newton-Mysovskikh theorem provides sufficient conditions for the semilocal convergence of Newton's method to a locally unique solution of an equation in a Banach space setting. It turns out that under weaker hypotheses and a more precise error analysis than before, weaker sufficient conditions can be obtained for the local as well as semilocal convergence of Newton's method. Error bounds on the distances involved as well as a larger radius of convergence are obtained. Some numerical examples are also provided.},
author = {Ioannis K. Argyros},
journal = {Applicationes Mathematicae},
keywords = {Newton's method; covariant Newton-Mysovskikh theorem; Banach space; local-semilocal convergence; radius of convergence; numerical examples},
language = {eng},
number = {3-4},
pages = {355-363},
title = {A weaker affine covariant Newton-Mysovskikh theorem for solving equations},
url = {http://eudml.org/doc/279402},
volume = {33},
year = {2006},
}

TY - JOUR
AU - Ioannis K. Argyros
TI - A weaker affine covariant Newton-Mysovskikh theorem for solving equations
JO - Applicationes Mathematicae
PY - 2006
VL - 33
IS - 3-4
SP - 355
EP - 363
AB - The Newton-Mysovskikh theorem provides sufficient conditions for the semilocal convergence of Newton's method to a locally unique solution of an equation in a Banach space setting. It turns out that under weaker hypotheses and a more precise error analysis than before, weaker sufficient conditions can be obtained for the local as well as semilocal convergence of Newton's method. Error bounds on the distances involved as well as a larger radius of convergence are obtained. Some numerical examples are also provided.
LA - eng
KW - Newton's method; covariant Newton-Mysovskikh theorem; Banach space; local-semilocal convergence; radius of convergence; numerical examples
UR - http://eudml.org/doc/279402
ER -