New third and fourth order nonlinear solvers for computing multiple roots

DOI10.1016/J.AMC.2011.04.063zbMath1220.65059OpenAlexW2078147424MaRDI QIDQ555372

Janak Raj Sharma, Rajni Sharma

Publication date: 22 July 2011

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

Full work available at URL: https://doi.org/10.1016/j.amc.2011.04.063

zbMATH Keywords

Newton's methodefficiencynonlinear equationsorder of convergencemultiple rootsrootfinding

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05)

Related Items (9)

On the convergence of Chebyshev's method for multiple polynomial zeros ⋮ An efficient family of optimal fourth-order iterative methods for finding multiple roots of nonlinear equations ⋮ Stability analysis of fourth-order iterative method for finding multiple roots of non-linear equations ⋮ A sixth order transformation method for finding multiple roots of nonlinear equations and basin attractors for various methods ⋮ General family of third order methods for multiple roots of nonlinear equations and basin attractors for various methods ⋮ Modified Chebyshev-Halley type method and its variants for computing multiple roots ⋮ A novel bi-parametric sixth order iterative scheme for solving nonlinear systems and its dynamics ⋮ On developing a novel sixth order transformation method for multiple roots and its basins of attraction ⋮ On the convergence of Halley's method for multiple polynomial zeros

Uses Software

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Cites Work

• Modified Jarratt method for computing multiple roots
• A new fourth-order iterative method for finding multiple roots of nonlinear equations
• New third order nonlinear solvers for multiple roots
• 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
• A family of fourth-order methods for solving nonlinear equations
• On Newton-type methods for multiple roots with cubic convergence
• 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
• Optimal Order of One-Point and Multipoint Iteration
• A variant of Newton's method with accelerated third-order convergence
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