Improved generalized differentiability conditions for Newton-like methods

Authors:
Ioannis K. Argyros;Saïd Hilout
Affiliations:
Cameron University, Department of Mathematics Sciences, Lawton, OK 73505, USA;Poitiers University, Laboratoire de Mathématiques et Applications, Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179, 86962 Futuroscope Chasseneuil Cedex, France
Venue:
Journal of Complexity
Year:
2010

Citing 8
Cited 4

A convergence theorem for Newton-like methods in Banach spaces

Numerische Mathematik
A note on the Kantorovich theorem for Newton iteration

Journal of Computational and Applied Mathematics
A new semilocal convergence theorem for Newton's method

Journal of Computational and Applied Mathematics
Iterative solution of nonlinear equations in several variables

Iterative solution of nonlinear equations in several variables
On the Newton-Kantorovich hypothesis for solving equations

Journal of Computational and Applied Mathematics
General local convergence theory for a class of iterative processes and its applications to Newton's method

Journal of Complexity
New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems

Journal of Complexity
On the weakening of the convergence of Newton's method using recurrent functions

Journal of Complexity

A unifying theorem for Newton's method on spaces with a convergence structure

Journal of Complexity
Local convergence analysis of the Gauss-Newton method under a majorant condition

Journal of Complexity
Extending the applicability of the Gauss---Newton method under average Lipschitz---type conditions

Numerical Algorithms
Local convergence analysis of inexact Gauss-Newton like methods under majorant condition

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We provide a semilocal convergence analysis for Newton-like methods using the @w-versions of the famous Newton-Kantorovich theorem (Argyros (2004) [1], Argyros (2007) [3], Kantorovich and Akilov (1982) [13]). In the special case of Newton's method, our results have the following advantages over the corresponding ones (Ezquerro and Hernaandez (2002) [10], Proinov (2010) [17]) under the same information and computational cost: finer error estimates on the distances involved; at least as precise information on the location of the solution, and weaker sufficient convergence conditions. Numerical examples, involving a Chandrasekhar-type nonlinear integral equation as well as a differential equation with Green's kernel are provided in this study.