Abstract

ARGYROS, Ioannis K. LOCAL CONVERGENCE FOR THE CURVE TRACING OF THE HOMOTOPY METHOD. Rev.colomb.mat. [online]. 2006, vol.40, n.2, pp.105-110. ISSN 0034-7426.

The local convergence of a Newton-method for the tracing of an implicitly defined smooth curve is analyzed. The domain of attraction is shown to be larger than in [6]. Moreover finer error bounds on the distances involved are obtained and quadratic instead of geometrical order of convergence is es- tablished. A numerical example is also provided where our results compare favourably with the corresponding ones in [6].

Keywords : Curve tracing; homotopy method; domain of attraction; radius of convergence; Newton-Kantorovich theorem/hypothesis; smooth curve; Moore-Penrose generalized inverse.

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