Accelerated methods of order \(2p\) for systems of nonlinear equations
type: Item
instance of: scholarly article
title: Accelerated methods of order \(2p\) for systems of nonlinear equations
zbMATH Open document ID: 1201.65078
author: Alicia Cordero
author: José L. Hueso
author: Eulalia Martínez
author: Juan Ramón Torregrosa Sánchez
published in: Journal of Computational and Applied Mathematics
publication date: 2010-02-12T00:00:00Z
review text: Applying the midpoint iteration method to the Newton method for solving the nonsingluar nonlinear problem \(F(x)=0\) with a smooth function \(F: D\subset {\mathbb R}^n\to {\mathbb R}^n\), the authors show that this new method has a convergence order of 5. They also consider approximations of the Jacobian matrix to reduce the computational work and use a few examples to illustrate the convergent orders of the proposed methods. It would be interesting to see a comparison of this method with a 2-step Newton and midpoint methods.
reviewed by: Zhen Mei
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 5669208
zbMATH Keywords: Newton method
zbMATH Keywords: system of nonlinear equations
zbMATH Keywords: fixed point iteration
zbMATH Keywords: convergence order
zbMATH Keywords: numerical examples
zbMATH Keywords: midpoint methods
MaRDI profile type: Publication
full work available at URL: j.cam.2009.11.018
OpenAlex ID: W1728782603
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DOI: 10.1016/J.CAM.2009.11.018
description: scientific article; zbMATH DE number 5669208