An improved algorithm due to laguerre for the solution of Kepler's equation

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)199-211
Number of pages13
JournalCelestial Mechanics
Volume39
Issue number2
DOIs
StatePublished - Jun 1 1986

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

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