On the convergence and application of Stirling's method

Ioannis K. Argyros. "On the convergence and application of Stirling's method." Applicationes Mathematicae 30.1 (2003): 109-119. <http://eudml.org/doc/279328>.

@article{IoannisK2003,
abstract = {We provide new sufficient convergence conditions for the local and semilocal convergence of Stirling's method to a locally unique solution of a nonlinear operator equation in a Banach space setting. In contrast to earlier results we do not make use of the basic restrictive assumption in [8] that the norm of the Fréchet derivative of the operator involved is strictly bounded above by 1. The study concludes with a numerical example where our results compare favorably with earlier ones.},
author = {Ioannis K. Argyros},
journal = {Applicationes Mathematicae},
keywords = {Stirling's method; Banach space; Fréchet derivative; majorizing sequence; Newton's method; convergence radius; numerical examples; fixed point equation; numerical operator},
language = {eng},
number = {1},
pages = {109-119},
title = {On the convergence and application of Stirling's method},
url = {http://eudml.org/doc/279328},
volume = {30},
year = {2003},
}

TY - JOUR
AU - Ioannis K. Argyros
TI - On the convergence and application of Stirling's method
JO - Applicationes Mathematicae
PY - 2003
VL - 30
IS - 1
SP - 109
EP - 119
AB - We provide new sufficient convergence conditions for the local and semilocal convergence of Stirling's method to a locally unique solution of a nonlinear operator equation in a Banach space setting. In contrast to earlier results we do not make use of the basic restrictive assumption in [8] that the norm of the Fréchet derivative of the operator involved is strictly bounded above by 1. The study concludes with a numerical example where our results compare favorably with earlier ones.
LA - eng
KW - Stirling's method; Banach space; Fréchet derivative; majorizing sequence; Newton's method; convergence radius; numerical examples; fixed point equation; numerical operator
UR - http://eudml.org/doc/279328
ER -