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Proyecciones (Antofagasta)

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Abstract

ARGYROS, IOANNIS K. CONVERGENCE OF NEWTON'S METHOD UNDER THE GAMMA CONDITION. Proyecciones (Antofagasta) [online]. 2006, vol.25, n.3, pp.293-306. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172006000300006.

We provide a semilocal as well as a local convergence analysis ofNewton's method using the gamma condition [1], [10], [11]. Usingmore precise majorizing sequences than before [4], [8]-[11] and underat least as weak hypotheses, we provide in the semilocal case: finererror bounds on the distances involved and an at least as precise informationon the location of the solution; in the local case: a largerradius of convergence

Keywords : Banach space; Newton's method; local/semilocalconvergence; Newton-Kantorovich theorem; Fréchet derivative; majorizingsequence; radius of convergence; gamma condition; analyticoperator.

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