On the gap between the semilocal convergence domains of two Newton methods

Ioannis K. Argyros. "On the gap between the semilocal convergence domains of two Newton methods." Applicationes Mathematicae 34.2 (2007): 193-204. <http://eudml.org/doc/279173>.

@article{IoannisK2007,
abstract = {We answer a question posed by Cianciaruso and De Pascale: What is the exact size of the gap between the semilocal convergence domains of the Newton and the modified Newton method? In particular, is it possible to close it? Our answer is yes in some cases. Using some ideas of ours and more precise error estimates we provide a semilocal convergence analysis for both methods with the following advantages over earlier approaches: weaker hypotheses; finer error bounds on the distances involved, and at least as precise information on the location of the solution; and a smaller gap between the two methods.},
author = {Ioannis K. Argyros},
journal = {Applicationes Mathematicae},
keywords = {Newton's method; modified Newton's method; Banach space; Hölder continuity; semilocal convergence; regular smoothness; Vertgeim condition, convergence domain},
language = {eng},
number = {2},
pages = {193-204},
title = {On the gap between the semilocal convergence domains of two Newton methods},
url = {http://eudml.org/doc/279173},
volume = {34},
year = {2007},
}

TY - JOUR
AU - Ioannis K. Argyros
TI - On the gap between the semilocal convergence domains of two Newton methods
JO - Applicationes Mathematicae
PY - 2007
VL - 34
IS - 2
SP - 193
EP - 204
AB - We answer a question posed by Cianciaruso and De Pascale: What is the exact size of the gap between the semilocal convergence domains of the Newton and the modified Newton method? In particular, is it possible to close it? Our answer is yes in some cases. Using some ideas of ours and more precise error estimates we provide a semilocal convergence analysis for both methods with the following advantages over earlier approaches: weaker hypotheses; finer error bounds on the distances involved, and at least as precise information on the location of the solution; and a smaller gap between the two methods.
LA - eng
KW - Newton's method; modified Newton's method; Banach space; Hölder continuity; semilocal convergence; regular smoothness; Vertgeim condition, convergence domain
UR - http://eudml.org/doc/279173
ER -