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

DOI10.1016/j.amc.2014.01.056zbMath1410.65143OpenAlexW2061263289MaRDI QIDQ1646100

Alicia Cordero, Carlos Andreu, Noelia Cambil, Juan Ramón Torregrosa Sánchez

Publication date: 22 June 2018

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2014.01.056

zbMATH Keywords

basin of attractioniterative methodnonlinear equationorder of convergenceefficiency indexderivative-free scheme

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05)

Related Items (13)

On developing a higher-order family of double-Newton methods with a bivariate weighting function ⋮ Some new weighted eighth-order variants of Steffensen-King's type family for solving nonlinear equations and its dynamics ⋮ IMPROVED BI-ACCELERATOR DERIVATIVE FREE WITH MEMORY FAMILY FOR SOLVING NONLINEAR EQUATIONS ⋮ A family of optimal quartic-order multiple-zero finders with a weight function of the principal \(k\)th root of a derivative-to-derivative ratio and their basins of attraction ⋮ A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points ⋮ An optimal eighth-order derivative-free family of Potra-Pták's method ⋮ Simplified existence and uniqueness conditions for the zeros and the concavity of the \(F\) and \(G\) functions of improved Gauss orbit determination from two position vectors ⋮ A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics ⋮ Higher-order derivative-free families of Chebyshev-Halley type methods with or without memory for solving nonlinear equations ⋮ Efficient derivative-free variants of Hansen-Patrick's family with memory for solving nonlinear equations ⋮ An optimal family of eighth-order simple-root finders with weight functions dependent on function-to-function ratios and their dynamics underlying extraneous fixed points ⋮ Constructing a family of optimal eighth-order modified Newton-type multiple-zero finders along with the dynamics behind their purely imaginary extraneous fixed points ⋮ An optimal eighth-order class of three-step weighted Newton's methods and their dynamics behind the purely imaginary extraneous fixed points

Cites Work

• A class of Steffensen type methods with optimal order of convergence
• An optimal Steffensen-type family for solving nonlinear equations
• Accurate fourteenth-order methods for solving nonlinear equations
• Two optimal eighth-order derivative-free classes of iterative methods
• On an efficient family of derivative free three-point methods for solving nonlinear equations
• Variants of Newton's method using fifth-order quadrature formulas
• A new technique to obtain derivative-free optimal iterative methods for solving nonlinear equations
• Gauss meets Newton again: how to make Gauss orbit determination from two position vectors more efficient and robust with Newton-Raphson iterations
• Optimal Order of One-Point and Multipoint Iteration
• Using accurate arithmetics to improve numerical reproducibility and stability in parallel applications
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