74913 20230126102832.0 doi 10.1007/s10569-017-9785-5 sideral 101614 ART-2017-101614 eng Elipe, A. Universidad de Zaragoza (orcid)0000-0001-5208-4494 An analysis of the convergence of Newton iterations for solving elliptic Kepler’s equation 2017 Access copy available to the general public Unrestricted In this note a study of the convergence properties of some starters (Formula presented.) in the eccentricity–mean anomaly variables for solving the elliptic Kepler’s equation (KE) by Newton’s method is presented. By using a Wang Xinghua’s theorem (Xinghua in Math Comput 68(225):169–186, 1999) on best possible error bounds in the solution of nonlinear equations by Newton’s method, we obtain for each starter (Formula presented.) a set of values (Formula presented.) that lead to the q-convergence in the sense that Newton’s sequence (Formula presented.) generated from (Formula presented.) is well defined, converges to the exact solution (Formula presented.) of KE and further (Formula presented.) holds for all (Formula presented.). This study completes in some sense the results derived by Avendaño et al. (Celest Mech Dyn Astron 119:27–44, 2014) by using Smale’s (Formula presented.)-test with (Formula presented.). Also since in KE the convergence rate of Newton’s method tends to zero as (Formula presented.), we show that the error estimates given in the Wang Xinghua’s theorem for KE can also be used to determine sets of q-convergence with (Formula presented.) for all (Formula presented.) and a fixed (Formula presented.). Some remarks on the use of this theorem to derive a priori estimates of the error (Formula presented.) after n Kepler’s iterations are given. Finally, a posteriori bounds of this error that can be used to a dynamical estimation of the error are also obtained. info:eu-repo/grantAgreement/ES/MICINN/MTM2013-47318-C2-1-P info:eu-repo/grantAgreement/ES/MINECO/2013-44217-R info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 2.121 2017 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS 30 / 103 = 0.291 2017 Q2 T1 ASTRONOMY & ASTROPHYSICS 34 / 66 = 0.515 2017 Q3 T2 1.092 2017 Applied Mathematics 2017 Q1 Computational Mathematics 2017 Q1 Modeling and Simulation 2017 Q1 Mathematical Physics 2017 Q1 Space and Planetary Science 2017 Q2 Astronomy and Astrophysics 2017 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Montijano, J.I. Universidad de Zaragoza (orcid)0000-0001-6120-4427 Rández, L. Universidad de Zaragoza (orcid)0000-0002-4238-3228 Calvo, M. Universidad de Zaragoza (orcid)0000-0002-3312-5710 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 129, 4 (2017), 415-432 Celest. mech. dyn. astron. Celestial Mechanics and Dynamical Astronomy 0923-2958 481191 http://zaguan.unizar.es/record/74913/files/texto_completo.pdf Postprint 57023 http://zaguan.unizar.es/record/74913/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:74913 articulos driver 2023-01-26-09:51:27 ARTICLE