# 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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