Convergence of starters for solving Kepler's equation via Smale's \(\alpha \)-test

DOI10.1007/s10569-016-9713-0zbMath1374.70023OpenAlexW2473516515MaRDI QIDQ1680395

Luis Rández, Antonio Elipe, Manuel Calvo, Juan I. Montijano

Publication date: 16 November 2017

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10569-016-9713-0

zbMATH Keywords

convergenceKepler's equationoptimal startersSmale's \(\alpha \)-test

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Two-body problems (70F05) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (3)

On the integral solution of elliptic Kepler's equation ⋮ An analysis of the convergence of Newton iterations for solving elliptic Kepler's equation ⋮ A monotonic starter for solving the hyperbolic Kepler equation by Newton's method

Cites Work

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• Sequential solution to Kepler's equation
• Solving Kepler's equation via Smale's \(\alpha\)-theory
• Fixed points, zeros and Newton's method
• On a theorem of S. Smale about Newton's method for analytic mappings
• The theory of Smale's point estimation and its applications
• Optimal starters for solving the elliptic Kepler's equation
• Fundamentals of astrodynamics and applications. With technical contributions by Wayne D. McClain.
• Approximate solutions of the hyperbolic Kepler equation

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