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.
\'A. Alberto Magre\~n\'an and Ioannis K. Argyros
Universidad Internacional De La Rioja, Cameron University
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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