How good are methods with memory for the solution of nonlinear equations?

DOI10.1007/S40324-016-0105-XzbMath1380.65088OpenAlexW2575361676MaRDI QIDQ1689279

Beny Neta, Changbum Chun

Publication date: 12 January 2018

Published in: S\(\vec{\text{e}}\)MA Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40324-016-0105-x

zbMATH Keywords

numerical examplebasin of attractionnonlinear equationsorder of convergencesimple rootsiterative methods with memory

Mathematics Subject Classification ID

General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Numerical computation of solutions to single equations (65H05)

Related Items (1)

Stability and applicability of iterative methods with memory

Cites Work

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• An analysis of a new family of eighth-order optimal methods
• On the new family of optimal eighth order methods developed by Lotfi et al.
• On the convergence of an optimal fourth-order family of methods and its dynamics
• An analysis of a family of Maheshwari-based optimal eighth order methods
• The basins of attraction of Murakami's fifth order family of methods
• On optimal fourth-order iterative methods free from second derivative and their dynamics
• Basin attractors for various methods
• Three-point methods with and without memory for solving nonlinear equations
• Basins of attraction for several methods to find simple roots of nonlinear equations
• Comparative study of eighth-order methods for finding simple roots of nonlinear equations
• A new family of optimal eighth order methods with dynamics for nonlinear equations
• Comparison of several families of optimal eighth order methods
• A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics
• On developing a higher-order family of double-Newton methods with a bivariate weighting function
• A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points
• A super-fast tri-parametric iterative method with memory
• Dynamics of the King and Jarratt iterations
• Dynamics of a family of third-order iterative methods that do not require using second derivatives
• 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
• Chaos in King's iterative family
• Basins of attraction for optimal eighth order methods to find simple roots of nonlinear equations
• Complex dynamics of derivative-free methods for nonlinear equations
• Optimal Order of One-Point and Multipoint Iteration
• Some Fourth Order Multipoint Iterative Methods for Solving Equations

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