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Kepler equation and accelerated Newton method. (English) Zbl 0998.65054
In the development of the work of {\it J. Gerlach} [SIAM Rev. 36, No. 2, 272-276 (1994; Zbl 0814.65046)] the author suggests a formula of order three and a proof of its convergence for the Newton method with applications to the resolution of a system of algebraic equations and to Kepler’s equation.

65H10Systems of nonlinear equations (numerical methods)
Full Text: DOI
[1] Danby, J. M.; Burkardt, T. M.: The solution of Kepler’s equation, III. Cel. mech. 31, 303-312 (1987) · Zbl 0647.70011
[2] Danby, J. M.; Burkardt, T. M.: The solution of Kepler’s equation, I. Cel. mech. 40, 95-107 (1983) · Zbl 0572.70014
[3] Demidovich, B.; Maron, I.: Éléments de calcule numérique. (1973)
[4] Ford, W. F.; Pennline, J. A.: Accelerated convergence in Newton’s method. SIAM rev. 38, 658-659 (1996) · Zbl 0863.65026
[5] Gerlach, J.: Accelerated convergence in Newton’s method. SIAM rev. 36, 272-276 (1994) · Zbl 0814.65046
[6] Mathews, J. H.: Numerical methods using Matlab. (1999)
[7] Ng, E. W.: A general algorithm for the solution of Kepler’s equation for elliptic orbits. Cel. mech. 20, 243 (1979) · Zbl 0417.70010
[8] Sanz-Serna, J. M.; Calvo, M. P.: Integración de sistemas hamiltonianos. SIAM rev. 38, 658-659 (1996)
[9] Wolfram, S.: Mathematica A system for doing mathematics by computer. (1991) · Zbl 0671.65002