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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Dr. Ioannis K. Argyros has degrees from University of Athens, Greece (1979, Bachelor in Mathematics), University of Georgia, Athens, Georgia, U.S.A. (M.Sc., 1983, Ph.D., 1984 in Mathematics). He is a professor of Mathematics with research interests in: Numerical Analysis, Numerical-Functional Analysis, Computational Mathematics, Optimization, Mathematical Economics, Mathematical Physics, Wavelet and Neural Networks.
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Argyros, I.K. On the convergence and application of Newton-like methods for analytic operators. JAMC 10, 41–50 (2002). https://doi.org/10.1007/BF02936204
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DOI: https://doi.org/10.1007/BF02936204