Constructing higher-order methods for obtaining the multiple roots of nonlinear equations

DOI10.1016/j.cam.2011.03.014zbMath1219.65048OpenAlexW2039381603MaRDI QIDQ548319

Xiaojian Zhou, Xin Chen, Yong-Zhong Song

Publication date: 28 June 2011

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

Full work available at URL: https://doi.org/10.1016/j.cam.2011.03.014

zbMATH Keywords

numerical examples iterative method nonlinear equations multiple roots convergence order efficiency index computer algebra system \texttt{Mathematica}

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Numerical computation of solutions to single equations (65H05) Complexity and performance of numerical algorithms (65Y20) Packaged methods for numerical algorithms (65Y15)

Related Items (56)

A general family of third order method for finding multiple roots ⋮ Optimal iterative methods for finding multiple roots of nonlinear equations using free parameters ⋮ An optimal scheme for multiple roots of nonlinear equations with eighth-order convergence ⋮ A stable class of modified Newton-like methods for multiple roots and their dynamics ⋮ Convergence radius of Osada's method under center-Hölder continuous condition ⋮ An optimal fourth-order family of methods for multiple roots and its dynamics ⋮ Dynamical behaviors of some iterative methods for multiple roots of nonlinear equations ⋮ A two-parameter family of fourth-order iterative methods with optimal convergence for multiple zeros ⋮ Comparative study of methods of various orders for finding repeated roots of nonlinear equations ⋮ A new family of methods for single and multiple roots ⋮ Optimal iterative methods for finding multiple roots of nonlinear equations using weight functions and dynamics ⋮ Multiplicity anomalies of an optimal fourth-order class of iterative methods for solving nonlinear equations ⋮ On developing fourth-order optimal families of methods for multiple roots and their dynamics ⋮ Convergence radius of Halley's method for multiple roots under center-Hölder continuous condition ⋮ Families of third and fourth order methods for multiple roots of nonlinear equations ⋮ On generalized Halley-like methods for solving nonlinear equations ⋮ On a numerical technique for finding multiple zeros and its dynamic ⋮ An efficient family of optimal fourth-order iterative methods for finding multiple roots of nonlinear equations ⋮ Development of cubically convergent iterative derivative free methods for computing multiple roots ⋮ An optimal reconstruction of Chebyshev-Halley type methods for nonlinear equations having multiple zeros ⋮ Iterative methods for multiple roots with memory using self-accelerating technique ⋮ Stability analysis of a family of optimal fourth-order methods for multiple roots ⋮ An efficient class of fourth-order derivative-free method for multiple-roots ⋮ On a family of high-order iterative methods under Kantorovich conditions and some applications ⋮ Construction and efficiency of multipoint root-ratio methods for finding multiple zeros ⋮ An Optimal Eighth-Order Scheme for Multiple Zeros of Univariate Functions ⋮ Basins of attraction for Zhou-Chen-song fourth order family of methods for multiple roots ⋮ 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 ⋮ Basins of attraction for several optimal fourth order methods for multiple roots ⋮ Symbolic computation and computer graphics as tools for developing and studying new root-finding methods ⋮ Comparing the basins of attraction for Kanwar-Bhatia-Kansal family to the best fourth order method ⋮ A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics ⋮ A class of computationally efficient numerical algorithms for locating multiple zeros ⋮ An eighth-order family of optimal multiple root finders and its dynamics ⋮ Multipoint methods for solving nonlinear equations: a survey ⋮ Constructing a family of optimal eighth-order modified Newton-type multiple-zero finders along with the dynamics behind their purely imaginary extraneous fixed points ⋮ On the convergence radius of the modified Newton method for multiple roots under the center-Hölder condition ⋮ An excellent numerical technique for multiple roots ⋮ A family of optimal eighth order iteration functions for multiple roots and its dynamics ⋮ On a two-step relaxed Newton-type method ⋮ Mean-based iterative methods for finding multiple roots in nonlinear chemistry problems ⋮ HIGHER-ORDER FAMILIES OF MULTIPLE ROOT FINDING METHODS SUITABLE FOR NON-CONVERGENT CASES AND THEIR DYNAMICS ⋮ Optimal eighth-order iterative methods for approximating multiple zeros of nonlinear functions ⋮ On an application of symbolic computation and computer graphics to root-finders: the case of multiple roots of unknown multiplicity ⋮ Local convergence balls for nonlinear problems with multiplicity and their extension to eighth-order convergence ⋮ 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 ⋮ On the optimality of some multi-point methods for finding multiple roots of nonlinear equation ⋮ On developing a novel sixth order transformation method for multiple roots and its basins of attraction ⋮ An efficient class of Traub-Steffensen-type methods for computing multiple zeros ⋮ A triparametric family of optimal fourth-order multiple-root finders and their dynamics ⋮ A new iterative method for finding the multiple roots of nonlinear equations ⋮ A new biparametric family of two-point optimal fourth-order multiple-root finders ⋮ An efficient family of optimal eighth-order multiple root finders ⋮ An efficient class of Traub-Steffensen-like seventh order multiple-root solvers with applications ⋮ Modified optimal class of Newton-like fourth-order methods for multiple roots

Uses Software

Mathematica

Cites Work

This page was built for publication: Constructing higher-order methods for obtaining the multiple roots of nonlinear equations