Analysis of Henrici's transformation for singular problems
type: Item
instance of: scholarly article
title: Analysis of Henrici's transformation for singular problems
zbMATH Open document ID: 1032.65051
author: M. Bellalij
published in: Numerical Algorithms
publication date: 2003-10-14T00:00:00Z
review text: In order to solve a system of nonlinear equations (1) \(F(x)=0\), where \( F:D\subset \mathbb{R}^{p}\rightarrow \mathbb{R}^{p}\) is differentiable and \(D\) is an open and convex subset of \(\mathbb{R}^{p}\), (1) is equivalently expressed in a fixed point form (2) \(x=G(x)\), where \(G\) is a certain iteration function. Then one uses the sequence of successive approximations defined by \(G\), i.e., the iterative scheme \[ x_{n+1}=G(x_{n}),n\geq 0 \tag{3} \] to obtain a fixed point of (2), that is, a solution of (1). When the iterative procedure (3) converges slowly, it is necessary to improve and accelerate its convergence. The present paper is devoted to the study of such an acceleration method, i.e., Henrici's transformation, which is the multivariable version of Aitken's \(\Delta ^{2}\) transformation.
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 1992771
zbMATH Keywords: system of nonlinear equations
zbMATH Keywords: fixed point
zbMATH Keywords: convergence acceleration
zbMATH Keywords: Henrici's transformation
zbMATH Keywords: method of successive approximation
zbMATH Keywords: Aitken's \(\Delta ^{2}\) transformation
reviewed by: Vasile Berinde
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1992771