Increasing the convergence rate of series
type: Item
instance of: scholarly article
title: Increasing the convergence rate of series
zbMATH Open document ID: 0633.65002
DOI: 10.1016/0096-3003(87)90031-2
author: I. M. Longman
published in: Applied Mathematics and Computation
publication date: 1987-01-01T00:00:00Z
review text: A method of accelerating the speed of convergence of a given series is presented and demonstrated by several examples. The main assumption is the existence of a specific asymptotic expansion of the terms in the series. In the examples the method works quite well. The paper does not contain proofs or theoretical backgrounds. The list of references only consists of papers of the author, except for the Handbook of mathematical functions (1967; Zbl 0171.385) by \textit{M. Abramowitz} and \textit{I. A. Stegun}. Other publications of similar content and close connection to the topic of the paper are not found under the references, and are not referred to in the text, e.g. \textit{J. Wimp} [SIAM J. Numer. Anal. 14, 194-204 (1977; Zbl 0355.65003)], \textit{A. H. Stroud} [Numerical quadrature and solution of ordinary differential equations (1974; Zbl 0298.65018), in particular p. 145-162], \textit{C. Brezinski} [Numer. Math. 35, 175-187 (1980; Zbl 0444.65001)], the reviewer [Proc. 5th South Afr. Symp. Numerical mathematics, Durban 1979, 1-20 (1979; Zbl 0435.65100)], the reviewer and \textit{G. Merz} [Praktische Mathematik. II. (1982; Zbl 0476.65001), in particular chapter 12].
Mathematics Subject Classification ID: 65B10
Mathematics Subject Classification ID: 65B05
zbMATH DE Number: 4030799
zbMATH Keywords: convergence acceleration
zbMATH Keywords: asymptotic expansion
MaRDI profile type: Publication
full work available at URL: 0096-3003(87)90031-2
OpenAlex ID: W2055393171
cites work: Q3661894
cites work: The summation of power series and Fourier series
cites work: The summation of series
cites work: The summation of Fourier, Chebyshev, and Legendre series
description: scientific article; zbMATH DE number 4030799