Approximation of artificial satellites' preliminary orbits: The efficiency challenge

Authors:
VíCtor Arroyo;Alicia Cordero;Juan R. Torregrosa
Affiliations:
-;-;-
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2011

Citing 3
Cited 0

Optimal Order of One-Point and Multipoint Iteration

Journal of the ACM (JACM)
Three-step iterative methods with eighth-order convergence for solving nonlinear equations

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New modifications of Potra-Pták's method with optimal fourth and eighth orders of convergence

Journal of Computational and Applied Mathematics

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Abstract

In this paper the problem of the determination of the preliminary orbit of a celestial body is studied. We compare the results obtained by the classical Gauss's method with those obtained by some higher-order iterative methods for solving nonlinear equations. The original problem of the determination of the preliminary orbits was posed by means of a nonlinear equation. We modify this equation in order to obtain a nonlinear system which describes the mentioned problem and we derive a new efficient iterative method for solving it. We also propose a new definition of optimal order of convergence for iterative methods for solving nonlinear systems.