A general semilocal convergence result for Newton’s method under centered conditions for the second derivative
José Antonio Ezquerro; Daniel González; Miguel Ángel Hernández
ESAIM: Mathematical Modelling and Numerical Analysis (2012)
- Volume: 47, Issue: 1, page 149-167
- ISSN: 0764-583X
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topEzquerro, José Antonio, González, Daniel, and Hernández, Miguel Ángel. "A general semilocal convergence result for Newton’s method under centered conditions for the second derivative." ESAIM: Mathematical Modelling and Numerical Analysis 47.1 (2012): 149-167. <http://eudml.org/doc/222132>.
@article{Ezquerro2012,
abstract = {From Kantorovich’s theory we present a semilocal convergence result for Newton’s method
which is based mainly on a modification of the condition required to the second derivative
of the operator involved. In particular, instead of requiring that the second derivative
is bounded, we demand that it is centered. As a consequence, we obtain a modification of
the starting points for Newton’s method. We illustrate this study with applications to
nonlinear integral equations of mixed Hammerstein type.},
author = {Ezquerro, José Antonio, González, Daniel, Hernández, Miguel Ángel},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Newton’s method; the Newton–Kantorovich theorem; semilocal convergence; majorizing sequence; a priori error estimates; Hammerstein’s integral equation; Newton's method; Newton-Kantorovich theorem; a priori error estimates; Hammerstein's integral equation},
language = {eng},
month = {7},
number = {1},
pages = {149-167},
publisher = {EDP Sciences},
title = {A general semilocal convergence result for Newton’s method under centered conditions for the second derivative},
url = {http://eudml.org/doc/222132},
volume = {47},
year = {2012},
}
TY - JOUR
AU - Ezquerro, José Antonio
AU - González, Daniel
AU - Hernández, Miguel Ángel
TI - A general semilocal convergence result for Newton’s method under centered conditions for the second derivative
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2012/7//
PB - EDP Sciences
VL - 47
IS - 1
SP - 149
EP - 167
AB - From Kantorovich’s theory we present a semilocal convergence result for Newton’s method
which is based mainly on a modification of the condition required to the second derivative
of the operator involved. In particular, instead of requiring that the second derivative
is bounded, we demand that it is centered. As a consequence, we obtain a modification of
the starting points for Newton’s method. We illustrate this study with applications to
nonlinear integral equations of mixed Hammerstein type.
LA - eng
KW - Newton’s method; the Newton–Kantorovich theorem; semilocal convergence; majorizing sequence; a priori error estimates; Hammerstein’s integral equation; Newton's method; Newton-Kantorovich theorem; a priori error estimates; Hammerstein's integral equation
UR - http://eudml.org/doc/222132
ER -
References
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