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. (C) 2014 Elsevier Inc. All rights reserved.This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02.Andreu Estellés, C.; Cambil Teba, N.; Cordero Barbero, A.; Torregrosa Sánchez, JR. (2014). A class of optimal eighth-order derivative-free methods for solving the Danchick-Gauss problem. Applied Mathematics and Computation. 232:237-246. https://doi.org/10.1016/j.amc.2014.01.056S23724623
