Modified Chebyshev-Halley type method and its variants for computing multiple roots

DOI10.1007/s11075-012-9551-4zbMath1263.65046OpenAlexW2086563658MaRDI QIDQ695044

Janak Raj Sharma, Rajni Sharma

Publication date: 20 December 2012

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-012-9551-4

zbMATH Keywords

Newton methodnonlinear equationsorder of convergencemultiple rootsChebyshev-Halley methodroot-finding

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05)

Related Items (9)

A family of fifth-order iterative methods for finding multiple roots of nonlinear equations ⋮ A two-parameter family of fourth-order iterative methods with optimal convergence for multiple zeros ⋮ The rate of multiplicity of the roots of nonlinear equations and its application to iterative methods ⋮ An optimal reconstruction of Chebyshev-Halley type methods for nonlinear equations having multiple zeros ⋮ A sixth order transformation method for finding multiple roots of nonlinear equations and basin attractors for various methods ⋮ Iterative methods for ill-conditioned roots ⋮ General family of third order methods for multiple roots of nonlinear equations and basin attractors for various methods ⋮ On developing a novel sixth order transformation method for multiple roots and its basins of attraction ⋮ A new biparametric family of two-point optimal fourth-order multiple-root finders

Uses Software

• Mathematica

Cites Work

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• Some second-derivative-free variants of Halley's method for multiple roots
• A family of root finding methods
• An optimal multiple root-finding method of order three
• On Newton-type methods for multiple roots with cubic convergence
• High-order nonlinear solver for multiple roots
• Extension of Murakami's high-order non-linear solver to multiple roots
• A family of multiopoint iterative functions for finding multiple roots of equations
• A higher order method for multiple zeros of nonlinear functions
• A family of Chebyshev-Halley type methods in Banach spaces

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