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
  • Mathematics
  • 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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