Extrapolation methods theory and practice
type: Item
instance of: scholarly article
title: Extrapolation methods theory and practice
zbMATH Open document ID: 0744.65004
author: Claude Brezinski
author: Michela Redivo-Zaglia
published in: Studies in Computational Mathematics
publication date: 1992-09-18T00:00:00Z
review text: There is a spectrum of convergence acceleration methods. At one end the methods are exercises in simple analysis; they are the subject of much academic activity; they are not of much use. At the other, the methods derive from results of considerable profundity in the theories of power and function series and of continued fractions; they suggest advances, which are relatively difficult to obtain, in these subjects; their numerical behaviour is subject to control and they are powerful. The book gives a pleasantly written and equitable treatment of the broad spectrum of methods. There are, of course, omissions. \textit{H. Rutishauser's} extension [Numer. Math. 5, 48--54 (1963; Zbl 0111.13001)] of Romberg's principle is not mentioned. Van Wijngaarden's transformation [for an accessible account, see \textit{J. W. Daniel}, Math. Comput. 23, 91--96 (1969; Zbl 0183.44101)] which is possibly the most successful known method for the treatment of extremely slowly convergent monotonic sequences is not dealt with. It might have been suggested that \textit{J. R. Schmidt}'s transformation [Philos. Mag., VII. Ser. 32, 369--383 (1941; Zbl 0061.27109)] may be derived in a few lines from a result contained in a classic paper [\textit{C. G. J. Jacobi}, J. Reine Angew. Math. 30, 127--156 (1845)] (not mentioned); in this way the theory of the transformation may be based upon the convergence theory of continued fractions which, apart from some recently published work of dubious utility, is not dealt with at all. Reference to the reviewer's paper [Arch. Math. 11, 223--236 (1960; Zbl 0096.09502)] which is of no practical use, might have been discarded in favour of another paper of the reviewer [Calcolo 15, No. 4, Suppl., 1--103 (1978; Zbl 0531.40002)] which contains many numerical examples and some convergence results. To have repaired these omissions would have destroyed the balance of the book. The literature index is selective. For example, the first author's paper [C. R. Acad. Sci., Par…
Mathematics Subject Classification ID: 65B05
Mathematics Subject Classification ID: 65-02
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65R10
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65C99
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65D25
Mathematics Subject Classification ID: 65B10
zbMATH DE Number: 52126
zbMATH Keywords: extrapolation methods
zbMATH Keywords: sequence transformation
zbMATH Keywords: monograph
zbMATH Keywords: numerical examples
zbMATH Keywords: floppy disk
zbMATH Keywords: programs
zbMATH Keywords: convergence acceleration
zbMATH Keywords: continued fractions
reviewed by: Peter Wynn
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 52126