On interpolation variants of Newton's method for functions of several variables
type: Item
instance of: scholarly article
title: On interpolation variants of Newton's method for functions of several variables
zbMATH Open document ID: 1201.65077
author: Alicia Cordero
author: Juan Ramón Torregrosa Sánchez
published in: Journal of Computational and Applied Mathematics
publication date: 2010-04-21T00:00:00Z
review text: Let \(F:D\subset R^n\to R^n\) be a sufficiently differentiable function. The convergence of the iterative method \[ x^{k+1}=x^k-(\sum_{h=1}^m A_hJ_F(\eta_h(x^k)))^{-1} F(x^k),\quad k\geq 0 \] towards a certain zero of \(F\) is discussed, via generalized Newton methods. Some numerical examples are given so as to illustrate the method.
reviewed by: Mihai Turinici
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 5696562
zbMATH Keywords: iteration
zbMATH Keywords: Newton method
zbMATH Keywords: order of convergence
zbMATH Keywords: Jacobian
zbMATH Keywords: efficiency index
zbMATH Keywords: interpolation
zbMATH Keywords: quadrature
zbMATH Keywords: fixed point iteration
zbMATH Keywords: sufficiently differentiable function
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: j.cam.2009.12.002
OpenAlex ID: W1966486703
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DOI: 10.1016/J.CAM.2009.12.002
description: scientific article; zbMATH DE number 5696562