Semilocal Convergence Newton Method Applied to Kepler Equation: New Results
M. A. Diloné *
Mathematics Institute, Universidad Autonoma de Santo Domingo, UASD, Dominican Republic.
J. M. Gutiérrez
Department of Mathematics and Computer Science, University of La Rioja, Spain.
E. Veras
Mathematics Institute, Universidad Autonoma de Santo Domingo, UASD, Dominican Republic.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Newton method, semilocal convergence theorem, kepler equation.