Improved Chebyshev-Halley methods with sixth and eighth order convergence

DOI10.1016/j.amc.2015.01.002zbMath1338.65134OpenAlexW2040618786MaRDI QIDQ299594

Janak Raj Sharma

Publication date: 22 June 2016

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

Full work available at URL: https://doi.org/10.1016/j.amc.2015.01.002

zbMATH Keywords

iterative methodsNewton methodcomputational efficiencyChebyshev-Halley methodoptimal order

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05)

Related Items

On the convergence of a higher order family of methods and its dynamics, Chaos and convergence of a family generalizing Homeier's method with damping parameters, 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, An Optimal Reconstruction of Chebyshev–Halley-Type Methods with Local Convergence Analysis, Ball comparison between two optimal eight-order methods under weak conditions, On the local convergence and the dynamics of Chebyshev-Halley methods with six and eight order of convergence, Ball convergence comparison between three iterative methods in Banach space under hypothese only on the first derivative, Different methods for solving STEM problems, Extended local convergence for some inexact methods with applications, Local results for an iterative method of convergence order six and efficiency index 1.8171

Uses Software

• Mathematica

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• An improvement of Chebyshev-Halley methods free from second derivative
• On optimal fourth-order iterative methods free from second derivative and their dynamics
• A family of optimal three-point methods for solving nonlinear equations using two parametric functions
• On Halley-type iterations with free second derivative
• Construction of optimal order nonlinear solvers using inverse interpolation
• Modifications of higher-order convergence for solving nonlinear equations
• A new sixth-order scheme for nonlinear equations
• Certain improvements of Newton's method with fourth-order convergence
• A family of three-point methods of optimal order for solving nonlinear equations
• Modified Chebyshev's method free from second derivative for non-linear equations
• Some second-derivative-free variants of Chebyshev-halley methods
• Fifth order implicit multipoint method for solving equations
• A note on the Halley method in Banach spaces
• Geometric constructions of iterative functions to solve nonlinear equations
• Some second-derivative-free variants of super-Halley method with fourth-order convergence
• A non-iterative method for solving non-linear equations
• The construction of rational iterative methods for solving nonlinear equations
• On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency
• A family of one-point iteration formulae for finding roots
• On a family of multipoint methods for non-linear equations
• A sixth-order family of methods for nonlinear equations
• A family of Chebyshev-Halley type methods in Banach spaces
• Optimal Order of One-Point and Multipoint Iteration
• Some efficient fourth order multipoint methods for solving equations
• Some Fourth Order Multipoint Iterative Methods for Solving Equations
• An acceleration of Newton's method: Super-Halley method
• A note on \(Q\)-order of convergence