On the convergence and application of Newton-like methods for analytic operators |
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Authors: | Ioannis K. Argyros |
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Affiliation: | 1. Department of Mathematics, Cameron University, 73505, Lawton, OK, U.S.A.
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Abstract: | We provide local and semilocal theorems for the convergence of Newton-like methods to a locally unique solution of an equation in a Banach space. The analytic property of the operator involved replaces the usual domain condition for Newton-like methods. In the case of the local results we show that the radius of convergence can be enlarged. A numerical example is given to justify our claim. This observation is important and finds applications in steplength selection in predictor-corrector continuation procedures. |
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