Estimating upper bounds on the limit points of majorizing sequences for Newton's method

Authors:
Ioannis K. Argyros;Saïd Hilout
Affiliations:
Department of Mathematical Sciences, Cameron University, Lawton, USA 73505;Laboratoire de Mathématiques et Applications, Poitiers University, Futuroscope Chasseneuil Cedex, France 86962
Venue:
Numerical Algorithms
Year:
2013

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Abstract

We present new sufficient conditions for the semilocal convergence of Newton's method to a locally unique solution of an equation in a Banach space setting. Upper bounds on the limit points of majorizing sequences are also given. Numerical examples are provided, where our new results compare favorably to earlier ones such as Argyros (J Math Anal Appl 298:374---397, 2004), Argyros and Hilout (J Comput Appl Math 234:2993-3006, 2010, 2011), Ortega and Rheinboldt (1970) and Potra and Pták (1984).