A family of optimal quartic-order multiple-zero finders with a weight function of the principal \(k\)th root of a derivative-to-derivative ratio and their basins of attraction
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Publication:2229042
DOI10.1016/J.MATCOM.2016.10.008OpenAlexW2549886050MaRDI QIDQ2229042
Beny Neta, Young Ik Kim, Young Hee Geum
Publication date: 19 February 2021
Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.matcom.2016.10.008
Related Items (6)
Comparative study of methods of various orders for finding repeated roots of nonlinear equations ⋮ How good are methods with memory for the solution of nonlinear equations? ⋮ Construction and efficiency of multipoint root-ratio methods for finding multiple zeros ⋮ Constructing a family of optimal eighth-order modified Newton-type multiple-zero finders along with the dynamics behind their purely imaginary extraneous fixed points ⋮ Mean-based iterative methods for finding multiple roots in nonlinear chemistry problems ⋮ COMPARATIVE STUDY OF METHODS OF VARIOUS ORDERS FOR FINDING SIMPLE ROOTS OF NONLINEAR EQUATIONS
Uses Software
Cites Work
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- Different anomalies in a Jarratt family of iterative root-finding methods
- A general family of third order method for finding multiple roots
- On optimal fourth-order iterative methods free from second derivative and their dynamics
- Basin attractors for various methods
- Basin attractors for various methods for multiple roots
- Basins of attraction for several methods to find simple roots of nonlinear equations
- On a family of Laguerre methods to find multiple roots of nonlinear equations
- Constructing higher-order methods for obtaining the multiple roots of nonlinear equations
- New optimal class of higher-order methods for multiple roots, permitting \(f'(x_{n})=0\)
- New third order nonlinear solvers for multiple roots
- Some fourth-order nonlinear solvers with closed formulae for multiple roots
- A third-order modification of Newton's method for multiple roots
- Cubic convergence of parameter-controlled Newton-secant method for multiple zeros
- Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions
- A family of root finding methods
- An optimal multiple root-finding method of order three
- On extraneous fixed-points of the basic family of iteration functions
- A class of optimal eighth-order derivative-free methods for solving the Danchick-Gauss problem
- Dynamics of the King and Jarratt iterations
- Dynamics of a family of third-order iterative methods that do not require using second derivatives
- Basins of attraction for Zhou-Chen-song fourth order family of methods for multiple roots
- Basins of attraction for several optimal fourth order methods for multiple roots
- Real qualitative behavior of a fourth-order family of iterative methods by using the convergence plane
- Chaos in King's iterative family
- A two-parameter family of fourth-order iterative methods with optimal convergence for multiple zeros
- On Newton-type methods for multiple roots with cubic convergence
- Basins of attraction for optimal eighth order methods to find simple roots of nonlinear equations
- Choosing weight functions in iterative methods for simple roots
- Complex dynamics of derivative-free methods for nonlinear equations
- High-order nonlinear solver for multiple roots
- Convergence of the Newton process to multiple solutions
- 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
- Optimal Order of One-Point and Multipoint Iteration
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