An Improved Algorithm due to Laguerre for the Solution of Kepler's Equation

Details An Improved Algorithm due to Laguerre for the Solution of Kepler's Equation An Improved Algorithm due to Laguerre for the Solution of Kepler's Equation

Jun 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986cemec..39..199c&link_type=abstract

Celestial Mechanics, Volume 39, Issue 2, pp.199-211

Computer Science

9

Scientific paper

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 higher-order Newton methods for the problem formulated in both conventional and universal variables and for both elliptic and hyperbolic orbits. In many thousands of trials the Laguerre method never failed to converge to the correct solution, even from exceptionally poor starting approximations. The non-local robustness and speed of convergence of the Laguerre method should make it the preferred method for the solution of Kepler's equation.

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