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http://dx.doi.org/10.14403/jcms.2012.25.2.267

LOCAL CONVERGENCE RESULTS FOR NEWTON'S METHOD

Argyros, Ioannis K. (Cameron University Department of Mathematical Sciences Lawton)
Hilout, Said (Poitiers University Laboratoire de Mathematiques et Applications Bd.)

Publication Information

Journal of the Chungcheong Mathematical Society / v.25, no.2, 2012 , pp. 267-275 More about this Journal

Abstract

We present new results for the local convergence of Newton's method to a unique solution of an equation in a Banach space setting. Under a flexible gamma-type condition [12], [13], we extend the applicability of Newton's method by enlarging the radius and decreasing the ratio of convergence. The results can compare favorably to other ones using Newton-Kantorovich and Lipschitz conditions [3]-[7], [9]-[13]. Numerical examples are also provided.

Keywords

Newton's method, Banach space; local convergence; radius of convergence; ratio of convergence; gamma-type condition; Lipschitz condition; Fr $\acute{e}$ chet-derivative;

Citations & Related Records

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