Appropriate Starter for Solving the Kepler's Equation

@article{Esmaelzadeh2014AppropriateSF,
  title={Appropriate Starter for Solving the Kepler's Equation},
  author={Reza Esmaelzadeh and Hossein Ghadiri},
  journal={International Journal of Computer Applications},
  year={2014},
  volume={89},
  pages={31-38}
}
This article, focuses on the methods that have been used for solving the Kepler’s equation for thirty years, then Kepler’s equation will be solved by Newton-Raphson’s method. For increasing the stability of Newton’s method, various guesses studied and the best of them introduced base on minimum number repetition of algorithm. At the end, after studying various guesses base on time of Implementation, one appropriate choice first guesses that increase the isotropy and decrease the time of… 
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References

SHOWING 1-10 OF 27 REFERENCES
On solving Kepler's equation
TLDR
This work attacks Kepler's equation with the unified derivation of all known bounds and several starting values, a proof of the optimality of these bounds, a very thorough numerical exploration of a large variety of starting values and solution techniques, and finally the best and simplest starting value/solution algorithm: M + e and Wegstein's secant modification of the method of successive substitutions.
Procedures for solving Kepler's equation
We review starting formulae and iteration processes for the solution of Kepler's equation, and give details of two complete procedures. The first has been in use for a number of years, but the second
Dynamic discretization method for solving Kepler’s equation
TLDR
This paper defines Kepler’s equation for the elliptical case and describes existing solution methods, and presents the dynamic discretization method and shows the results of a comparative analysis, demonstrating that, for the conditions of the tests, dynamicDiscretization performs the best.
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
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 solution of Kepler's equation, I
Methods of iteration are discussed in relation to Kepler's equation, and various initial ‘guesses’ are considered, with possible strategies for choosing them. Several of these are compared; the
A general algorithm for the solution of Kepler's equation for elliptic orbits
An efficient algorithm is presented for the solution of Kepler's equationf(E)=E−M−e sinE=0, wheree is the eccentricity,M the mean anomaly andE the eccentric anomaly. This algorithm is based on simple
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
A Solution of Kepler’s Equation
The present study deals with a traditional physical problem: the solution of the Kepler’s equation for all conics (ellipse, hyperbola or parabola). Solution of the universal Kepler’s equation in
A simple, efficient starting value for the iterative solution of Kepler's equation
A simple starting value for the iterative solution of Kepler's equation in the elliptic case is presented. This value is then compared against five other starting values for 3750 test cases. In
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