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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

ARGYROS, IOANNIS K  and  HILOUT, SAÏD. ON THE LOCAL CONVERGENCE OF A NEWTON-TYPE METHOD IN BANACH SPACES UNDER A GAMMA-TYPE CONDITION. Proyecciones (Antofagasta) [online]. 2008, vol.27, n.1, pp.1-14. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172008000100001.

We provide a local convergence analysis for a Newton-type method to approximate a locally unique solution of an operator equation in Banach spaces. The local convergence of this method was studied in the elegant work by Werner in [11], using information on the domain of the operator. Here, we use information only at a point and a gamma-type condition [4], [10]. It turns out that our radius of convergence is larger, and more general than the corresponding one in [10]. Moreover the same can hold true when our radius is compared with the ones given in [9] and [11]. A numerical example is also provided

Keywords : Banach space; Newton-type method; convergence; gamma-type condition; local convergence; Fréchet-derivative; radius of convergence.

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