Inexact Newton methods and recurrent functions

Ioannis K. Argyros, and Saïd Hilout. "Inexact Newton methods and recurrent functions." Applicationes Mathematicae 37.1 (2010): 113-126. <http://eudml.org/doc/280008>.

@article{IoannisK2010,
abstract = {We provide a semilocal convergence analysis for approximating a solution of an equation in a Banach space setting using an inexact Newton method. By using recurrent functions, we provide under the same or weaker hypotheses: finer error bounds on the distances involved, and an at least as precise information on the location of the solution as in earlier papers. Moreover, if the splitting method is used, we show that a smaller number of inner/outer iterations can be obtained. Furthermore, numerical examples are provided using polynomial, integral and differential equations.},
author = {Ioannis K. Argyros, Saïd Hilout},
journal = {Applicationes Mathematicae},
keywords = {Banach space; Inexact Newton method; Recurrent functions; Majorizing sequence; Residual; Semilocal convergence; Center - Lipschitz condition; nonlinear operator equation; numerical examples},
language = {eng},
number = {1},
pages = {113-126},
title = {Inexact Newton methods and recurrent functions},
url = {http://eudml.org/doc/280008},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Ioannis K. Argyros
AU - Saïd Hilout
TI - Inexact Newton methods and recurrent functions
JO - Applicationes Mathematicae
PY - 2010
VL - 37
IS - 1
SP - 113
EP - 126
AB - We provide a semilocal convergence analysis for approximating a solution of an equation in a Banach space setting using an inexact Newton method. By using recurrent functions, we provide under the same or weaker hypotheses: finer error bounds on the distances involved, and an at least as precise information on the location of the solution as in earlier papers. Moreover, if the splitting method is used, we show that a smaller number of inner/outer iterations can be obtained. Furthermore, numerical examples are provided using polynomial, integral and differential equations.
LA - eng
KW - Banach space; Inexact Newton method; Recurrent functions; Majorizing sequence; Residual; Semilocal convergence; Center - Lipschitz condition; nonlinear operator equation; numerical examples
UR - http://eudml.org/doc/280008
ER -