On the convergence of the secant method under the gamma condition |
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| Authors: | Ioannis K. Argyros |
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| Affiliation: | (1) Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA |
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| Abstract: | We provide sufficient convergence conditions for the Secant method of approximating a locally unique solution of an operator equation in a Banach space. The main hypothesis is the gamma condition first introduced in [10] for the study of Newton’s method. Our sufficient convergence condition reduces to the one obtained in [10] for Newton’s method. A numerical example is also provided. |
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| Keywords: | Banach space Secant method Newton’ s method Gamma condition majorizing sequence semilocal convergence radius of convergence Newton-Kantorovich theorem |
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