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ISSN : 1226-0657

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Vol.14 No.3

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On a Quadratically Convergent Iterative Method Using Divided Differencesof Order One

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2007, v.14 no.3, pp.203-221
Argyros, Ioannis K.
Argyros,, I. K. (2007). On a Quadratically Convergent Iterative Method Using Divided Differencesof Order One. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 14(3), 203-221.

Abstract

We introduce a new two-point iterative method to approximate solutions of nonlinear operator equations. The method uses only divided differences of order one, and two previous iterates. However in contrast to the Secant method which is of order 1.618..., our method is of order two. A local and a semilocal convergence analysis is provided based on the majorizing principle. Finally the monotone convergence of the method is explored on partially ordered topological spaces. Numerical examples are also provided where our results compare favorably to earlier ones [1], [4], [5], [19].

keywords
Banach space, POTL-space, majorant principle, Secant method, local/semilocal/monotone convergence, radius of convergence, Lipschitz conditions, divided differences

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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