Recurrence relations for Chebyshev-type methods
type: Item
instance of: scholarly article
title: Recurrence relations for Chebyshev-type methods
zbMATH Open document ID: 0952.47050
published in: Applied Mathematics and Optimization
publication date: 2000-02-23T00:00:00Z
review text: The main aim of this paper is to construct a new iterative method to solve the equation \(F(x)= 0\). This iteration, defined by: \[ \Gamma_n= F'(x_n)^{-1},\quad T(x_n)= \textstyle{{1\over 2}} \Gamma_nA\Gamma_n F(x_n),\quad x_{n+1}= x_n- [I+ T(x_n)]\Gamma_nF(x_n),\quad n\geq 0 \] (where \(I\) is the identity operator on \(X\) and \(A: X\times X\to Y\) is a bilinear operator which satisfies \(\|A\|= \alpha\) \((\alpha\geq 0)\)) has similar operatorial costs and works under the same conditions as Newton's method. Two examples are also given, proving that the velocity of the convergence increases and better error estimates are provided.
reviewed by: Adrian Petruşel
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 65J15
zbMATH DE Number: 1406321
zbMATH Keywords: recurrence relations
zbMATH Keywords: a priori error bounds
zbMATH Keywords: iterative method
zbMATH Keywords: Newton's method
author: J. A. Ezquerro
author: M. A. Hernández
MaRDI profile type: Publication
full work available at URL: s002459911012
OpenAlex ID: W2071146872
DOI: 10.1007/S002459911012
description: scientific article; zbMATH DE number 1406321