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

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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).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Cameron University, Lawton, OK, 73505, USA

    Ioannis K. Argyros

  2. Laboratoire de Mathématiques et Applications, Poitiers University, Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179, 86962, Futuroscope Chasseneuil Cedex, France

    Saïd Hilout

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  1. Ioannis K. Argyros
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  2. Saïd Hilout
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Correspondence to Ioannis K. Argyros.

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Argyros, I.K., Hilout, S. Estimating upper bounds on the limit points of majorizing sequences for Newton’s method. Numer Algor 62, 115–132 (2013). https://doi.org/10.1007/s11075-012-9570-1

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