A method solving kepler's equation without transcendental function evaluations

@article{Fukushima1996AMS,
  title={A method solving kepler's equation without transcendental function evaluations},
  author={Toshio Fukushima},
  journal={Celestial Mechanics and Dynamical Astronomy},
  year={1996},
  volume={66},
  pages={309-319}
}
  • T. Fukushima
  • Published 1996
  • Physics
  • Celestial Mechanics and Dynamical Astronomy
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 expansion. A combination of these was applied to solving Kepler's equation for the elliptic case. The resulting method requires no evaluation of transcendental functions. Numerical measurements showed that, in the case of Intel Pentium processor, the new method is three times as fast as the original… 
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Kepler Equation solver
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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.
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
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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