A class of optimal eighth-order derivative-free methods for solving the Danchick–Gauss problem
Applied Mathematics and Computation, 2014•Elsevier
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.
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.
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.
Elsevier
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