Abstract

ARGYROS, IOANNIS K.. On the semilocal convergence of a fast two-step Newton method. Rev.colomb.mat. [online]. 2008, vol.42, n.1, pp.15-24. ISSN 0034-7426.

We provide a semilocal convergence analysis for a cubically convergent two-step Newton method (2) recently introduced by H. Homeier [8], [9], and also studied by A. Özban [13]. In contrast to the above works we examine the semilocal convergence of the method in a Banach space setting, instead of the local in the real or complex number case. A comparison is given with a two step Newton--like method using the same information.

Keywords : Two-step Newton method; Newton method; Banach space; majorizing sequence; Newton--Kantorovich hypothesis; semilocal convergence; Fréchet-derivative.

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