Some second-derivative-free variants of Chebyshev-halley methods

DOI10.1016/j.amc.2007.02.105zbMath1193.65054OpenAlexW1971201974MaRDI QIDQ990451

Changbum Chun

Publication date: 1 September 2010

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

Full work available at URL: https://doi.org/10.1016/j.amc.2007.02.105

zbMATH Keywords

Newton's methoditerative methodsnonlinear equationsorder of convergenceChebyshev-halley methods

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05)

Related Items (17)

An improvement of Chebyshev-Halley methods free from second derivative ⋮ Improved Chebyshev-Halley methods with sixth and eighth order convergence ⋮ Modified Chebyshev-Halley methods free from second derivative ⋮ A new modified secant-like method for solving nonlinear equations ⋮ An optimal fourth-order family of modified Cauchy methods for finding solutions of nonlinear equations and their dynamical behavior ⋮ Improved Chebyshev-Halley family of methods with seventh and eighth order of convergence for simple roots ⋮ An optimal reconstruction of Chebyshev-Halley type methods for nonlinear equations having multiple zeros ⋮ Steffensen type methods for solving nonlinear equations ⋮ An Optimal Reconstruction of Chebyshev–Halley-Type Methods with Local Convergence Analysis ⋮ Some new variants of Cauchy's methods for solving nonlinear equations ⋮ Derivative free algorithm for solving nonlinear equations ⋮ Dynamics of a family of Chebyshev-Halley type methods ⋮ Constructing third-order derivative-free iterative methods ⋮ A class of third order iterative Kurchatov-Steffensen (derivative free) methods for solving nonlinear equations ⋮ Local Convergence of a Family of Iterative Methods with Sixth and Seventh Order Convergence Under Weak Conditions ⋮ Zero-finder methods derived from Obreshkov's techniques ⋮ New iterative methods for solving nonlinear problems with one and several unknowns

Cites Work

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• On Halley-type iterations with free second derivative
• Modified Halley's method free from second derivative
• Modified Chebyshev's method free from second derivative for non-linear equations
• Some variants of Chebyshev-halley methods free from second derivative
• The Jarratt method in Banach space setting
• Second-derivative-free variant of the Chebyshev method for nonlinear equations
• A composite third order Newton-Steffensen method for solving nonlinear equations
• A family of Chebyshev-Halley type methods in Banach spaces
• An acceleration of Newton's method: Super-Halley method

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