Extrapolation methods
type: Item
instance of: scholarly article
title: Extrapolation methods
zbMATH Open document ID: 0814.65001
DOI: 10.1016/0168-9274(94)00015-8
published in: Applied Numerical Mathematics
publication date: 1995-06-18T00:00:00Z
review text: This paper is really an introduction to the book [Extrapolation methods, theory and practice (1991; Zbl 0744.65004)], by the same authors. The paper begins with a discussion of terminology and notation, using Aitken's method as an example. The sequence transformation for Aitken's algorithm is then generalized to produce the Shanks transformation, and there is a brief discussion of the \(\varepsilon\)-algorithm for computing the Shanks transformation. This leads to a discussion of the possibility of a universal transformation for accelerating the convergence of all convergent sequences. The concept of remanence is introduced to discuss sets of sequences that are non-accelerable. The paper concludes with some general comments about extrapolation methods and their applications.
Mathematics Subject Classification ID: 65B05
zbMATH DE Number: 699074
zbMATH Keywords: epsilon algorithm
zbMATH Keywords: convergence acceleration
zbMATH Keywords: Aitken's algorithm
zbMATH Keywords: Shanks transformation
zbMATH Keywords: remanence
zbMATH Keywords: extrapolation methods
author: Claude Brezinski
author: Michela Redivo-Zaglia
reviewed by: A. Genz
MaRDI profile type: Publication
full work available at URL: 0168-9274(94)00015-8
OpenAlex ID: W2914282094
cites work: Extrapolation methods theory and practice
description: scientific article; zbMATH DE number 699074