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ISSN : 1226-0657

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Vol.15 No.1
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APPROXIMATING SOLUTIONS OF EQUATIONSBY COMBINING NEWTON-LIKE METHODS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2008, v.15 no.1, pp.35-45
Argyros, Ioannis K.
Argyros,, I. K. (2008). APPROXIMATING SOLUTIONS OF EQUATIONSBY COMBINING NEWTON-LIKE METHODS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 15(1), 35-45.
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Abstract

In cases sufficient conditions for the semilocal convergence of Newtonlike methods are violated, we start with a modified Newton-like method (whose weaker convergence conditions hold) until we stop at a certain finite step. Then using as a starting guess the point found above we show convergence of the Newtonlike method to a locally unique solution of a nonlinear operator equation in a Banach space setting. A numerical example is also provided.

keywords
Newton-like method, modified Newton-like method, Banach space, semilocal convergence, Frechet-derivative, Newton-Kantorovich-type hypotheses

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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