Semilocal Convergence Newton Method Applied to Kepler Equation: New Results

摘要

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.