Some second-derivative-free variants of Halley's method for multiple roots

DOI10.1016/j.amc.2009.08.010zbMath1181.65070OpenAlexW2065622098WikidataQ57704081 ScholiaQ57704081MaRDI QIDQ1039687

Housen Li, Sheng-Guo Li, Li-Zhi Cheng

Publication date: 23 November 2009

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

Full work available at URL: https://doi.org/10.1016/j.amc.2009.08.010

zbMATH Keywords

algorithmcomparison of methodsnumerical examplesHalley's methodroot findingMultiple rootsNonlinear equationNew iterative methods

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05)

Related Items (10)

A family of fifth-order iterative methods for finding multiple roots of nonlinear equations ⋮ Derivative free algorithm for solving nonlinear equations ⋮ Constructing third-order derivative-free iterative methods ⋮ Modified Chebyshev-Halley type method and its variants for computing multiple roots ⋮ New third and fourth order nonlinear solvers for computing multiple roots ⋮ Convergence radius of the modified Newton method for multiple zeros under Hölder continuous derivative ⋮ On developing a novel sixth order transformation method for multiple roots and its basins of attraction ⋮ A new fifth-order iterative method free from second derivative for solving nonlinear equations ⋮ New families of third-order iterative methods for finding multiple roots ⋮ On the convergence of Halley's method for multiple polynomial zeros

Cites Work

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• On Halley-type iterations with free second derivative
• Modified Halley's method free from second derivative
• New third order nonlinear solvers for multiple roots
• New families of nonlinear third-order solvers for finding multiple roots
• A third-order modification of Newton's method for multiple roots
• A family of root finding methods
• An optimal multiple root-finding method of order three
• High-order nonlinear solver for multiple roots
• A family of multiopoint iterative functions for finding multiple roots of equations
• A higher order method for multiple zeros of nonlinear functions

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