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Bull. Korean Math. Soc. 2015; 52(3): 865-880

Printed May 31, 2015

https://doi.org/10.4134/BKMS.2015.52.3.865

Copyright © The Korean Mathematical Society.

Expanding the applicability of secant method with applications

\'A. Alberto Magre\~n\'an and Ioannis K. Argyros

Universidad Internacional De La Rioja, Cameron University

Abstract

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We present new sufficient convergence criteria for the convergence of the secant-method to a locally unique solution of a nonlinear equation in a Banach space. Our idea uses Lipschitz and center--Lipschitz instead of just Lipschitz conditions in the convergence analysis. The new convergence criteria can always be weaker than the corresponding ones in earlier studies. Numerical examples are also provided in this study to solve equations in cases not possible before.

Keywords: secant method, Banach space, majorizing sequence, divided difference, Fr\'echet--derivative

MSC numbers: 47H17, 49M15, 65H10, 65B05, 65G99, 65N30

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