A uniparametric family of three-step eighth-order multipoint iterative methods for simple roots

DOI10.1016/j.aml.2011.01.002zbMath1215.65092OpenAlexW2026646824MaRDI QIDQ2430053

Young Ik Kim, Young Hee Geum

Publication date: 5 April 2011

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2011.01.002

zbMATH Keywords

convergencenumerical experimentsefficiency indexmultipoint methodeighth-order convergenceuniparametric family

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05) Complexity and performance of numerical algorithms (65Y20)

Related Items (18)

Some new bi-accelerator two-point methods for solving nonlinear equations ⋮ A variant of Steffensen-King's type family with accelerated sixth-order convergence and high efficiency index: dynamic study and approach ⋮ Several iterative methods with memory using self-accelerators ⋮ Computers in mathematical research: the study of three-point root-finding methods ⋮ Optimal eighth order convergent iteration scheme based on Lagrange interpolation ⋮ A family of three-point methods of Ostrowski's type for solving nonlinear equations ⋮ Iterative methods for solving nonlinear equations with finitely many roots in an interval ⋮ Three-point methods with and without memory for solving nonlinear equations ⋮ A new optimal eighth-order family of iterative methods for the solution of nonlinear equations ⋮ A family of fast derivative-free fourth-order multipoint optimal methods for nonlinear equations ⋮ A triparametric family of three-step optimal eighth-order methods for solving nonlinear equations ⋮ Multipoint methods for solving nonlinear equations: a survey ⋮ 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 ⋮ Comparative study of eighth-order methods for finding simple roots of nonlinear equations ⋮ An optimal family of fast 16th-order derivative-free multipoint simple-root finders for nonlinear equations ⋮ On generalized biparametric multipoint root finding methods with memory ⋮ Two optimal general classes of iterative methods with eighth-order ⋮ An optimal eighth-order class of three-step weighted Newton's methods and their dynamics behind the purely imaginary extraneous fixed points

Uses Software

• Mathematica

Cites Work

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• A family of three-point methods of optimal order for solving nonlinear equations
• A class of three-point root-solvers of optimal order of convergence
• Three-step iterative methods with eighth-order convergence for solving nonlinear equations
• A fourth order iterative method for solving nonlinear equations
• A new family of eighth-order iterative methods for solving nonlinear equations
• Optimal Order of One-Point and Multipoint Iteration
• Some Fourth Order Multipoint Iterative Methods for Solving Equations
• A Family of Fourth Order Methods for Nonlinear Equations

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