A convergence analysis of Newton-like methods for singular equations using outer or generalized inverses

Ioannis K. Argyros. "A convergence analysis of Newton-like methods for singular equations using outer or generalized inverses." Applicationes Mathematicae 32.1 (2005): 37-49. <http://eudml.org/doc/279662>.

@article{IoannisK2005,
abstract = {The Newton-Kantorovich approach and the majorant principle are used to provide new local and semilocal convergence results for Newton-like methods using outer or generalized inverses in a Banach space setting. Using the same conditions as before, we provide more precise information on the location of the solution and on the error bounds on the distances involved. Moreover since our Newton-Kantorovich-type hypothesis is weaker than before, we can cover cases where the original Newton-Kantorovich hypothesis is violated.},
author = {Ioannis K. Argyros},
journal = {Applicationes Mathematicae},
keywords = {Newton-type method; iteration; convergence; Banach space; generalized inverse; Newton-Kantorovich hypothesis; Newton-Kantorovich theorem; nonlinear operator equation},
language = {eng},
number = {1},
pages = {37-49},
title = {A convergence analysis of Newton-like methods for singular equations using outer or generalized inverses},
url = {http://eudml.org/doc/279662},
volume = {32},
year = {2005},
}

TY - JOUR
AU - Ioannis K. Argyros
TI - A convergence analysis of Newton-like methods for singular equations using outer or generalized inverses
JO - Applicationes Mathematicae
PY - 2005
VL - 32
IS - 1
SP - 37
EP - 49
AB - The Newton-Kantorovich approach and the majorant principle are used to provide new local and semilocal convergence results for Newton-like methods using outer or generalized inverses in a Banach space setting. Using the same conditions as before, we provide more precise information on the location of the solution and on the error bounds on the distances involved. Moreover since our Newton-Kantorovich-type hypothesis is weaker than before, we can cover cases where the original Newton-Kantorovich hypothesis is violated.
LA - eng
KW - Newton-type method; iteration; convergence; Banach space; generalized inverse; Newton-Kantorovich hypothesis; Newton-Kantorovich theorem; nonlinear operator equation
UR - http://eudml.org/doc/279662
ER -