Design of high-order iterative methods for nonlinear systems by using weight function procedure
type: Item
instance of: scholarly article
title: Design of high-order iterative methods for nonlinear systems by using weight function procedure
zbMATH Open document ID: 1433.65093
DOI: 10.1155/2015/289029
author: Santiago Artidiello
author: Alicia Cordero
author: Juan Ramón Torregrosa Sánchez
author: María P. Vassileva
published in: Abstract and Applied Analysis
publication date: 2018-08-29T00:00:00Z
review text: Summary: We present two classes of iterative methods whose orders of convergence are four and five, respectively, for solving systems of nonlinear equations, by using the technique of weight functions in each step. Moreover, we show an extension to higher order, adding only one functional evaluation of the vectorial nonlinear function. We perform numerical tests to compare the proposed methods with other schemes in the literature and test their effectiveness on specific nonlinear problems. Moreover, some real basins of attraction are analyzed in order to check the relation between the order of convergence and the set of convergent starting points.
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 6929081
Wikidata QID: Q59101583
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/289029
OpenAlex ID: W1606083881
cites work: Using accurate arithmetics to improve numerical reproducibility and stability in parallel applications
cites work: A variant of Newton's method with accelerated third-order convergence
cites work: Some new variants of Newton's method.
cites work: Accelerated Convergence in Newton’s Method
cites work: Variants of Newton's method for functions of several variables
cites work: Variants of Newton's method using fifth-order quadrature formulas
cites work: On interpolation variants of Newton's method for functions of several variables
cites work: Third-order methods from quadrature formulae for solving systems of nonlinear equations.
cites work: Pseudocomposition: A technique to design predictor-corrector methods for systems of nonlinear equations
cites work: Q5732060
cites work: Some Fourth Order Multipoint Iterative Methods for Solving Equations
cites work: An efficient fourth order weighted-Newton method for systems of nonlinear equations
cites work: An efficient fifth order method for solving systems of nonlinear equations
cites work: A modified Newton-Jarratt's composition
cites work: Q3932219
description: scientific article; zbMATH DE number 6929081