Some unusual results on extrapolation methods
type: Item
instance of: scholarly article
title: Some unusual results on extrapolation methods
zbMATH Open document ID: 1469.65010
published in: Numerical Algorithms
publication date: 2020-07-15T00:00:00Z
review text: The paper discusses two fundamental questions in connection with extrapolation methods. Assuming a convergent sequence \((S_n)\) is given, the essence of such methods is that one may attempt to extrapolate the sequence, i.e., to construct, by the well known Shanks transformation, a second sequence \((T_n)\), say, that has the same limit but that hopefully converges faster than the original sequence. The first main result of the paper is a set of necessary conditions that the original sequence \((S_n)\) must satisfy in order for the sequence \((T_n)\) to converge faster than \((S_n)\). Based on these conditions, the authors then construct stopping criteria allowing the user to terminate the acceleration procedure when a best possible precision is reached. The second main result then deals with an ``inverse problem'' in the sense that properties of the transformed sequence \((T_n)\) are prescribed and it is then demonstrated which properties the original sequence \((S_n)\) must have in order for these properties to be present.
reviewed by: Kai Diethelm
Mathematics Subject Classification ID: 65B05
Mathematics Subject Classification ID: 41A21
zbMATH DE Number: 7221098
zbMATH Keywords: acceleration methods
zbMATH Keywords: sequence transformations
zbMATH Keywords: necessary conditions
zbMATH Keywords: stopping criteria
zbMATH Keywords: prescribed behavior
zbMATH Keywords: Padé approximation
author: Claude Brezinski
author: Michela Redivo-Zaglia
describes a project that uses: mctoolbox
describes a project that uses: EPSfun
MaRDI profile type: Publication
full work available at URL: s11075-019-00782-y
OpenAlex ID: W2964917236
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DOI: 10.1007/S11075-019-00782-Y
description: scientific article; zbMATH DE number 7221098