The solution of Kepler's equation, I

@article{Danby1983TheSO,
  title={The solution of Kepler's equation, I},
  author={J. M. Anthony Danby and T. M. Burkardt},
  journal={Celestial mechanics},
  year={1983},
  volume={31},
  pages={95-107}
}
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 method of iteration used in the comparisons has local convergence of the fourth order. 
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Complex-variable analysis is used to develop an exact solution to Kepler's equation, for both elliptic and hyperbolic orbits. The method is based on basic properties of canonical solutions to
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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