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

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:
2011

Citing 3
Cited 0

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
Improved generalized differentiability conditions for Newton-like methods

Journal of Complexity

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a semilocal convergence theorem for Newton's method (NM) on spaces with a convergence structure. Using our new idea of recurrent functions, we provide a tighter analysis, with weaker hypotheses than before and with the same computational cost as for Argyros (1996, 1997, 1997, 2007) [1-3,5], Meyer (1984, 1987, 1992) [13-15]. Numerical examples are provided for solving equations in cases not covered before.