A class of optimal eighth-order derivative-free methods for solving the Danchick–Gauss problem

Carlos Andreu, Noelia Cambil, Alicia Cordero and Juan R. Torregrosa

Applied Mathematics and Computation, 2014, vol. 232, issue C, 237-246

Abstract: A derivative-free optimal eighth-order family of iterative methods for solving nonlinear equations is constructed using weight functions approach with divided first order differences. Its performance, along with several other derivative-free methods, is studied on the specific problem of Danchick’s reformulation of Gauss’ method of preliminary orbit determination. Numerical experiments show that such derivative-free, high-order methods offer significant advantages over both, the classical and Danchick’s Newton approach.

Keywords: Nonlinear equation; Iterative method; Derivative-free scheme; Order of convergence; Basin of attraction; Efficiency index (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:232:y:2014:i:c:p:237-246

DOI: 10.1016/j.amc.2014.01.056

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