King-type derivative-free iterative families: real and memory dynamics
type: Item
instance of: scholarly article
title: King-type derivative-free iterative families: real and memory dynamics
zbMATH Open document ID: 1378.65111
DOI: 10.1155/2017/2713145
author: Alicia Cordero
author: Francisco I. Chicharro
author: Juan Ramón Torregrosa Sánchez
author: María P. Vassileva
published in: Complexity
publication date: 2018-01-03T00:00:00Z
review text: Summary: A biparametric family of derivative-free optimal iterative methods of order four, for solving nonlinear equations, is presented. From the error equation of this class, different families of iterative schemes with memory can be designed increasing the order of convergence up to six. The real stability analysis of the biparametric family without memory is made on quadratic polynomials, finding areas in the parametric plane with good performance. Moreover, in order to study the real behavior of the parametric class with memory, we associate it with a discrete multidimensional dynamical system. By analyzing the fixed and critical points of its vectorial rational function, we can select those methods with best stability properties.
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 39B12
zbMATH DE Number: 6821573
zbMATH Keywords: nonlinear equations
zbMATH Keywords: derivative-free optimal iterative methods
zbMATH Keywords: stability analysis
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/2713145
OpenAlex ID: W2766343750
cites work: Complex dynamics of derivative-free methods for nonlinear equations
cites work: Dynamics and fractal dimension of Steffensen-type methods
cites work: Derivative free iterative methods for nonlinear systems
cites work: A new tool to study real dynamics: the convergence plane
cites work: Real qualitative behavior of a fourth-order family of iterative methods by using the convergence plane
cites work: Optimal Order of One-Point and Multipoint Iteration
cites work: Q5723445
cites work: Q5732060
cites work: Q5326192
cites work: Multipoint methods for solving nonlinear equations: a survey
cites work: A multidimensional dynamical approach to iterative methods with memory
cites work: Complex analytic dynamics on the Riemann sphere
cites work: Q3993502
cites work: Dynamics of a fifth-order iterative method
cites work: Stability of King's family of iterative methods with memory
cites work: Q4899294
cites work: Graphic and numerical comparison between iterative methods
description: scientific article; zbMATH DE number 6821573