Inexact Newton method under weak and center-weak Lipschitz conditions

I. K. Argyros, and S. K. Khattri. "Inexact Newton method under weak and center-weak Lipschitz conditions." Applicationes Mathematicae 40.2 (2013): 237-258. <http://eudml.org/doc/279963>.

@article{I2013,
abstract = {The paper develops semilocal convergence of Inexact Newton Method INM for approximating solutions of nonlinear equations in Banach space setting. We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis. The results obtained compare favorably with earlier ones in at least the case of Newton's Method (NM). Numerical examples, where our convergence criteria are satisfied but the earlier ones are not, are also explored.},
author = {I. K. Argyros, S. K. Khattri},
journal = {Applicationes Mathematicae},
keywords = {inexact Newton method; Banach space; semilocal convergence; weak and center-weak Lipschitz condition; recurrent functions; Kantorovich hypotheses; numerical examples; nonlinear operator equation; Fréchet continuously differentiable operator},
language = {eng},
number = {2},
pages = {237-258},
title = {Inexact Newton method under weak and center-weak Lipschitz conditions},
url = {http://eudml.org/doc/279963},
volume = {40},
year = {2013},
}

TY - JOUR
AU - I. K. Argyros
AU - S. K. Khattri
TI - Inexact Newton method under weak and center-weak Lipschitz conditions
JO - Applicationes Mathematicae
PY - 2013
VL - 40
IS - 2
SP - 237
EP - 258
AB - The paper develops semilocal convergence of Inexact Newton Method INM for approximating solutions of nonlinear equations in Banach space setting. We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis. The results obtained compare favorably with earlier ones in at least the case of Newton's Method (NM). Numerical examples, where our convergence criteria are satisfied but the earlier ones are not, are also explored.
LA - eng
KW - inexact Newton method; Banach space; semilocal convergence; weak and center-weak Lipschitz condition; recurrent functions; Kantorovich hypotheses; numerical examples; nonlinear operator equation; Fréchet continuously differentiable operator
UR - http://eudml.org/doc/279963
ER -