000074913 001__ 74913
000074913 005__ 20230126102832.0
000074913 0247_ $$2doi$$a10.1007/s10569-017-9785-5
000074913 0248_ $$2sideral$$a101614
000074913 037__ $$aART-2017-101614
000074913 041__ $$aeng
000074913 100__ $$0(orcid)0000-0001-5208-4494$$aElipe, A.$$uUniversidad de Zaragoza
000074913 245__ $$aAn analysis of the convergence of Newton iterations for solving elliptic Kepler’s equation
000074913 260__ $$c2017
000074913 5060_ $$aAccess copy available to the general public$$fUnrestricted
000074913 5203_ $$aIn 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.
000074913 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/MTM2013-47318-C2-1-P$$9info:eu-repo/grantAgreement/ES/MINECO/2013-44217-R
000074913 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000074913 590__ $$a2.121$$b2017
000074913 591__ $$aMATHEMATICS, INTERDISCIPLINARY APPLICATIONS$$b30 / 103 = 0.291$$c2017$$dQ2$$eT1
000074913 591__ $$aASTRONOMY & ASTROPHYSICS$$b34 / 66 = 0.515$$c2017$$dQ3$$eT2
000074913 592__ $$a1.092$$b2017
000074913 593__ $$aApplied Mathematics$$c2017$$dQ1
000074913 593__ $$aComputational Mathematics$$c2017$$dQ1
000074913 593__ $$aModeling and Simulation$$c2017$$dQ1
000074913 593__ $$aMathematical Physics$$c2017$$dQ1
000074913 593__ $$aSpace and Planetary Science$$c2017$$dQ2
000074913 593__ $$aAstronomy and Astrophysics$$c2017$$dQ2
000074913 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000074913 700__ $$0(orcid)0000-0001-6120-4427$$aMontijano, J.I.$$uUniversidad de Zaragoza
000074913 700__ $$0(orcid)0000-0002-4238-3228$$aRández, L.$$uUniversidad de Zaragoza
000074913 700__ $$0(orcid)0000-0002-3312-5710$$aCalvo, M.$$uUniversidad de Zaragoza
000074913 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000074913 773__ $$g129, 4 (2017), 415-432$$pCelest. mech. dyn. astron.$$tCelestial Mechanics and Dynamical Astronomy$$x0923-2958
000074913 8564_ $$s481191$$uhttps://zaguan.unizar.es/record/74913/files/texto_completo.pdf$$yPostprint
000074913 8564_ $$s57023$$uhttps://zaguan.unizar.es/record/74913/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
000074913 909CO $$ooai:zaguan.unizar.es:74913$$particulos$$pdriver
000074913 951__ $$a2023-01-26-09:51:27
000074913 980__ $$aARTICLE