Different anomalies in a Jarratt family of iterative root-finding methods
From MaRDI portal
Publication:272533
DOI10.1016/j.amc.2014.01.037zbMath1334.65083OpenAlexW1971939073MaRDI QIDQ272533
Publication date: 20 April 2016
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2014.01.037
stabilityiterative methodsparameter spacecomplex dynamicsnonlinear problemsbasins of attractionJarratt family
Related Items (only showing first 100 items - show all)
CMMSE2017: on two classes of fourth- and seventh-order vectorial methods with stable behavior ⋮ Secant-like methods for solving nonlinear models with applications to chemistry ⋮ Second derivative free sixth order continuation method for solving nonlinear equations with applications ⋮ Ball convergence of a sixth-order Newton-like method based on means under weak conditions ⋮ Dynamical analysis of iterative methods for nonlinear systems or how to deal with the dimension? ⋮ Extended ball convergence for a seventh order derivative free class of algorithms for nonlinear equations ⋮ Complex dynamics of a sixth and seventh order family of root finding methods ⋮ Highly efficient family of iterative methods for solving nonlinear models ⋮ Newton's method on generalized Banach spaces ⋮ On the new family of optimal eighth order methods developed by Lotfi et al. ⋮ A new tool to study real dynamics: the convergence plane ⋮ On the convergence of an optimal fourth-order family of methods and its dynamics ⋮ A variant of Steffensen-King's type family with accelerated sixth-order convergence and high efficiency index: dynamic study and approach ⋮ An analysis of a family of Maheshwari-based optimal eighth order methods ⋮ Comparative study of methods of various orders for finding repeated roots of nonlinear equations ⋮ Extended iterative schemes based on decomposition for nonlinear models ⋮ On the comparison of inventory replenishment policies with time-varying stochastic demand for the paper industry ⋮ Third-degree anomalies of Traub's method ⋮ On the convergence of a higher order family of methods and its dynamics ⋮ The basins of attraction of Murakami's fifth order family of methods ⋮ A stable family with high order of convergence for solving nonlinear equations ⋮ On developing a higher-order family of double-Newton methods with a bivariate weighting function ⋮ A study on the local convergence and complex dynamics of Kou's family of iterative methods ⋮ On the election of the damped parameter of a two-step relaxed Newton-type method ⋮ Local convergence and a chemical application of derivative free root finding methods with one parameter based on interpolation ⋮ Chaos and convergence of a family generalizing Homeier's method with damping parameters ⋮ On developing fourth-order optimal families of methods for multiple roots and their dynamics ⋮ On the convergence of inexact two-point Newton-like methods on Banach spaces ⋮ Extended Traub-Woźniakowski convergence and complexity of Newton iteration in Banach space ⋮ A family of higher order iterations free from second derivative for nonlinear equations in \(\mathbb{R}\) ⋮ Widening basins of attraction of optimal iterative methods ⋮ Local convergence and complex dynamics of a uni-parametric family of iterative schemes ⋮ Convergence for iterative methods on Banach spaces of a convergence structure with applications to fractional calculus ⋮ Ball convergence theorems and the convergence planes of an iterative method for nonlinear equations ⋮ A complex dynamical approach of Chebyshev's method ⋮ Long-term orbit dynamics viewed through the yellow main component in the parameter space of a family of optimal fourth-order multiple-root finders ⋮ Local convergence for some high convergence order Newton-like methods with frozen derivatives ⋮ Ball convergence for an eighth order efficient method under weak conditions in Banach spaces ⋮ Improved Chebyshev-Halley family of methods with seventh and eighth order of convergence for simple roots ⋮ A note on ``Convergence radius of Osada's method under Hölder continuous condition ⋮ Stability analysis of a parametric family of seventh-order iterative methods for solving nonlinear systems ⋮ An efficient optimal family of sixteenth order methods for nonlinear models ⋮ Dynamical aspects of some convex acceleration methods as purely iterative algorithm for Newton's maps ⋮ Local convergence of a multi-step high order method with divided differences under hypotheses on the first derivative ⋮ Ball comparison between two optimal eight-order methods under weak conditions ⋮ On the local convergence of Kung-Traub's two-point method and its dynamics. ⋮ On the local convergence and the dynamics of Chebyshev-Halley methods with six and eight order of convergence ⋮ A biparametric extension of King's fourth-order methods and their dynamics ⋮ A multidimensional dynamical approach to iterative methods with memory ⋮ 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 ⋮ A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points ⋮ Dynamics of a multipoint variant of Chebyshev-Halley's family ⋮ Symbolic computation and computer graphics as tools for developing and studying new root-finding methods ⋮ Study of iterative methods through the Cayley quadratic test ⋮ Local convergence of an optimal eighth order method under weak conditions ⋮ Newton-type methods on generalized Banach spaces and applications in fractional calculus ⋮ Local convergence of an efficient high convergence order method using hypothesis only on the first derivative ⋮ Local convergence analysis of an eighth order scheme using hypothesis only on the first derivative ⋮ Extending the convergence domain of the secant and Moser method in Banach space ⋮ Graphical representations for the homogeneous bivariate Newton's method ⋮ Comparison of several families of optimal eighth order methods ⋮ Comparing the basins of attraction for Kanwar-Bhatia-Kansal family to the best fourth order method ⋮ Ball convergence comparison between three iterative methods in Banach space under hypothese only on the first derivative ⋮ Basins of attraction for several third order methods to find multiple roots of nonlinear equations ⋮ A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics ⋮ An analysis of a Khattri's 4th order family of methods ⋮ On the dynamics of a triparametric family of optimal fourth-order multiple-zero finders with a weight function of the principal \(m\)th root of a function-to-function ratio ⋮ Improving the domain of parameters for Newton's method with applications ⋮ Local convergence and the dynamics of a two-point four parameter Jarratt-like method under weak conditions ⋮ Constructing a family of optimal eighth-order modified Newton-type multiple-zero finders along with the dynamics behind their purely imaginary extraneous fixed points ⋮ Unifying semilocal and local convergence of Newton's method on Banach space with a convergence structure ⋮ On the approximation of \(m\)th power divided differences preserving the local order of convergence ⋮ Multidimensional stability analysis of a family of biparametric iterative methods: CMMSE2016 ⋮ A Krasnosel'skii-Zincenko-type method in \(K\)-normed spaces for solving equations ⋮ Comparative study of eighth-order methods for finding simple roots of nonlinear equations ⋮ Different methods for solving STEM problems ⋮ Extended local convergence for some inexact methods with applications ⋮ Dynamical analysis on cubic polynomials of damped Traub's method for approximating multiple roots ⋮ Local convergence of iterative methods for solving equations and system of equations using weight function techniques ⋮ Extending the applicability of the super-Halley-like method using \(\omega\)-continuous derivatives and restricted convergence domains ⋮ Construction of stable and globally convergent schemes for the matrix sign function ⋮ On the convergence, dynamics and applications of a new class of nonlinear system solvers ⋮ Ball convergence for an inverse free jarratt-type method under Hölder conditions ⋮ A study of dynamics via Möbius conjugacy map on a family of sixth-order modified Newton-like multiple-zero finders with bivariate polynomial weight functions ⋮ A unified convergence analysis for some iterative algorithms with applications to fractional calculus ⋮ Ball convergence for second derivative free methods in Banach space ⋮ Generalized \(g\)-fractional calculus of Canavati-type and secant-like methods ⋮ Extending the applicability of the inexact Newton-HSS method for solving large systems of nonlinear equations ⋮ Ball convergence of some iterative methods for nonlinear equations in Banach space under weak conditions ⋮ Local convergence of fourth and fifth order parametric family of iterative methods in Banach spaces ⋮ The dynamical analysis of a uniparametric family of three-point optimal eighth-order multiple-root finders under the Möbius conjugacy map on the Riemann sphere ⋮ Convergence analysis for single point Newton-type iterative schemes ⋮ An efficient high order iterative scheme for large nonlinear systems with dynamics ⋮ On the complexity of choosing majorizing sequences for iterative procedures ⋮ Unified convergence for multi-point super Halley-type methods with parameters in Banach space ⋮ Local convergence of a family of weighted-Newton methods ⋮ Some higher-order iteration functions for solving nonlinear models ⋮ Extended three step sixth order Jarratt-like methods under generalized conditions for nonlinear equations ⋮ Derivative free fourth order solvers of equations with applications in applied disciplines ⋮ A new fourth-order family for solving nonlinear problems and its dynamics
Cites Work
- Unnamed Item
- Unnamed Item
- 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
- A construction of attracting periodic orbits for some classical third-order iterative methods
- Dynamics of a new family of iterative processes for quadratic polynomials
- Dynamics of the King and Jarratt iterations
- Chaotic dynamics of a third-order Newton-type method
- Chaos in King's iterative family
- Complex dynamics of derivative-free methods for nonlinear equations
- Dynamics of a family of Chebyshev-Halley type methods
- The Mandelbrot Set, the Farey Tree, and the Fibonacci Sequence
This page was built for publication: Different anomalies in a Jarratt family of iterative root-finding methods