Dynamical techniques for analyzing iterative schemes with memory
type: Item
instance of: scholarly article
title: Dynamical techniques for analyzing iterative schemes with memory
zbMATH Open document ID: 1398.65098
DOI: 10.1155/2018/1232341
author: Neha Choubey
author: Alicia Cordero
author: J. P. Jaiswal
author: Juan Ramón Torregrosa Sánchez
published in: Complexity
publication date: 2018-09-27T00:00:00Z
review text: Summary: We construct a new biparametric three-point method with memory to highly improve the computational efficiency of its original partner, without adding functional evaluations. In this way, through different estimations of self-accelerating parameters, we have modified an existing seventh-order method. The parameters have been defined by Hermite interpolating polynomial that allows the accelerating effect. In particular, the \(R\)-order of the proposed iterative method with memory is increased from seven to ten. A real multidimensional analysis of the stability of this method with memory is made, in order to study its dependence on the initial estimations. Taking into account that usually iterative methods with memory are more stable than their derivative-free partners and the obtained results in this study, the behavior of this scheme shows to be excellent, but for a small domain. Numerical examples and comparison are also provided, confirming the theoretical results.
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 6944893
zbMATH Keywords: biparametric three-point method with memory
zbMATH Keywords: estimations of self-accelerating parameters
zbMATH Keywords: Hermite interpolating polynomial
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/1232341
OpenAlex ID: W2810694964
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Wikidata QID: Q129646904
description: scientific article; zbMATH DE number 6944893