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ISSN : 1226-0657

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Vol.17 No.4

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ON THE SEMILOCAL CONVERGENCE OF THE GAUSS-NEWTON METHOD USING RECURRENT FUNCTIONS

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
2010, v.17 no.4, pp.307-319
Argyros, Ioannis K.
Hilout, Said
Argyros,, I. K. , & Hilout,, S. (2010). ON THE SEMILOCAL CONVERGENCE OF THE GAUSS-NEWTON METHOD USING RECURRENT FUNCTIONS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 17(4), 307-319.

Abstract

We provide a new semilocal convergence analysis of the Gauss-Newton method (GNM) for solving nonlinear equation in the Euclidean space. Using our new idea of recurrent functions, and a combination of center-Lipschitz, Lipschitz conditions, we provide under the same or weaker hypotheses than before [7]-[13], a tighter convergence analysis. The results can be extented in case outer or generalized inverses are used. Numerical examples are also provided to show that our results apply, where others fail [7]-[13].

keywords
Gauss-Newton method, semilocal convergence, Frechet-derivative, More-Penrose pseudo-inverse

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

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