An efficient code to solve the Kepler equation. Elliptic case

@article{RaposoPulido2017AnEC,
  title={An efficient code to solve the Kepler equation. Elliptic case},
  author={Virginia Raposo-Pulido and Jes{\'u}s Pel{\'a}ez},
  journal={Monthly Notices of the Royal Astronomical Society},
  year={2017},
  volume={467},
  pages={1702-1713}
}
A new approach for solving Kepler equation for elliptical orbits is developed in this paper. This new approach takes advantage of the very good behaviour of the modified Newton?Raphson method when the initial seed is close to the looked for solution. To determine a good initial seed the eccentric anomaly domain [0, ?] is discretized in several intervals and for each one of these intervals a fifth degree interpolating polynomial is introduced. The six coefficients of the polynomial are obtained… 
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Comment on ‘An efficient code to solve the Kepler equation: elliptic case’
In a recent MNRAS article, Raposo-Pulido and Pelaez (RPP) designed a scheme for obtaining very close seeds for solving the elliptic Kepler equation with the classical and modified Newton–Raphson
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References

SHOWING 1-10 OF 14 REFERENCES
A method solving kepler's equation without transcendental function evaluations
We developed two approximations of the Newton-Raphson method. The one is a sort of discretization, namely to search an approximate solution on pre-specified grid points. The other is a Taylor series
An improved algorithm due to laguerre for the solution of Kepler's equation
A root-finding method due to Laguerre (1834–1886) is applied to the solution of the Kepler problem. The speed of convergence of this method is compared with that of Newton's method and several
An analytical solution for Kepler's problem
In this paper, we present a framework which provides an analytical (i.e. infinitely differentiable) transformation between spatial coordinates and orbital elements for the solution of the
Kepler Equation solver
TLDR
Kepler's Equation is solved over the entire range of elliptic motion by a fifth-order refinement of the solution of a cubic equation, and requires only four transcendental function evaluations.
The hyperbolic Kepler equation (and the elliptic equation revisited)
A procedure is developed that, in two iterations, solves the hyperbolic Kepler's equation in a very efficient manner, and to an accuracy that proves to be always better than 10−20 (relative
Long-term changes in the semimajor axes of the outer planets
One of the oldest problems of celestial mechanics is that of the long-term behaviour of the semimajor axes a of the planetary orbits. Analytical theories1,2 predict periodic variations in a, some of
Solving Kepler's equation with high efficiency and accuracy
We present a method for solving Kepler's equation for elliptical orbits that represents a gain in efficiency and accuracy compared with those currently in use. The gain is obtained through a starter
Chaotic behaviour in the newton iterative function associated with kepler's equation
The chaotic behaviour observed when Newton's method is used to solve Kepler's equation is analysed using methods borrowed from chaos theory. The result of the analysis is compared with previous
An introduction to the mathematics and methods of astrodynamics
Part 1 Hypergeometric Functions and Elliptic Integrals: Some Basic Topics In Analytical Dynamics The Problem of Two Bodies Two-Body Orbits and the Initial-Value Problem Solving Kepler's Equation
Ideal frames for perturbed Keplerian motions
Cartan's exterior calculus is used to refer a perturbed Keplerian motion to an ideal frame by means of either the Eulerian parameters or the Eulerian angles, in which case the equations are given a
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