New Kantorovich-type conditions for Halley's method

Resumen

New semilocal convergence results of Newton-Kantorovich type for the Halley method are presented, where the usual convergence conditions, which appears in the literature, are relaxed. Firstly, it is supposed that the second derivative F" of a nonlinear operator F satisfies parallel to F" (x(0))parallel to <= alpha instead of parallel to F" (x)parallel to <= M, for all x in a subset of the domain of F, where alpha and M are positive real constants. Secondly, fewer convergence conditions are required than all the existing ones until now. (c) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.