Semilocal Convergence Newton Method Applied to Kepler Equation: New Results
M. A. Diloné, J. M. Gutiérrez, E. Veras
Journal of Advances in Mathematics and Computer Science · pp. 1–13 · Published 31 Mar 2017
10.9734/BJMCS/2017/30928Abstract
The aim of this paper is to consider as a starting point the value E0 = π in the theorems of semilocal convergence of Kantorovich, Gutiérrez, α−theory of Smale and the α−theory of Wang-Zhao, to compare the convergence conditions obtained. Once set E0, one should calculate the parameters listed in the statement of these theorem. So, we will generalize the study of Diloné-Gutiérrez for the case E0 = M. Numeric and graphic calculations were obtained by applying Mathematica V10.
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