Improved local convergence of Newton's method under weak majorant condition

Authors:
Ioannis K. Argyros;SaïD Hilout
Affiliations:
Cameron University, Department of Mathematical 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 Computational and Applied Mathematics
Year:
2012

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Abstract

We provide a local convergence analysis for Newton's method under a weak majorant condition in a Banach space setting. Our results provide under the same information a larger radius of convergence and tighter error estimates on the distances involved than before [14]. Special cases and numerical examples are also provided in this study.