Modified families of Newton, Halley and Chebyshev methods

DOI10.1016/j.amc.2007.02.119zbMath1193.65065OpenAlexW2078862683MaRDI QIDQ990484

Sushil Kumar Tomar, Vinay Kanwar

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.2007.02.119

zbMATH Keywords

Newton's methodHalley's methodorder of convergenceChebyshev's methodnon-linear equations

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05)

Related Items (19)

The convergence ball and error analysis of the two-step secant method ⋮ Efficient families of Newton's method and its variants suitable for non-convergent cases ⋮ A new modified secant-like method for solving nonlinear equations ⋮ Geometrically constructed families of Newton's method for unconstrained optimization and nonlinear equations ⋮ A family of derivative-free methods for nonlinear equations ⋮ Derivative free algorithm for solving nonlinear equations ⋮ One-point Newton-type iterative methods: a unified point of view ⋮ Modified families of multi-point iterative methods for solving nonlinear equations ⋮ On new third-order convergent iterative formulas ⋮ Constructing third-order derivative-free iterative methods ⋮ On some cubic convergence iterative formulae without derivatives for solving nonlinear equations ⋮ Simple geometric constructions of quadratically and cubically convergent iterative functions to solve nonlinear equations ⋮ Note on a cubically convergent Newton-type method under weak conditions ⋮ Several new third-order iterative methods for solving nonlinear equations ⋮ Exponentially fitted variants of Euler's method for ODEs ⋮ New third-order method for solving systems of nonlinear equations ⋮ Exponentially fitted variants of Newton's method with quadratic and cubic convergence ⋮ Zero-finder methods derived from Obreshkov's techniques ⋮ Optimal equi-scaled families of Jarratt's method

Uses Software

• KELLEY

Cites Work

• On a class of quadratic convergence iteration formulae without derivatives
• Classroom Note:Geometry and Convergence of Euler's and Halley's Methods
• On the Geometry of Halley's Method
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