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http://dx.doi.org/10.14403/jcms.2015.28.4.513

ON A LOCAL CHARACTERIZATION OF SOME NEWTON-LIKE METHODS OF R-ORDER AT LEAST THREE UNDER WEAK CONDITIONS IN BANACH SPACES

Argyros, Ioannis K. (Department of Mathematicsal Sciences Cameron University)
George, Santhosh (Department of Mathematical and Computational Sciences National Institute of Technology Karnataka)

Publication Information

Journal of the Chungcheong Mathematical Society / v.28, no.4, 2015 , pp. 513-523 More about this Journal

Abstract

We present a local convergence analysis of some Newton-like methods of R-order at least three in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second $Fr{\acute{e}}chet$ -derivative of the operator involved. These conditions are weaker that the corresponding ones given by Hernandez, Romero [10] and others [1], [4]-[9] requiring hypotheses up to the third $Fr{\acute{e}}chet$ derivative. Numerical examples are also provided in this study.

Keywords

Newton-like methods; R-order of convergence; Banach space; local convergence; $Fr{\acute{e}}chet$ -derivative;

Citations & Related Records

Reference

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