On the stability of a class of convergence acceleration methods for power series
type: Item
instance of: scholarly article
title: On the stability of a class of convergence acceleration methods for power series
zbMATH Open document ID: 0552.65002
DOI: 10.1007/BF01934909
author: Sven-Åke Gustafson
published in: BIT
publication date: 1984-01-01T00:00:00Z
review text: Power series having the form \(F(z)=\sum^{\infty}_{r=0}z^ rf_ rc_ r\) are studied where z is a complex number, and assuming i) F has a positive radius of convergence R. ii) \(f(z)=\sum^{\infty}_{r=0}z^ rf_ r,\) is known as analytical expression, and iii) \(c_ r=\int^{b}_{a}t^ rd\alpha (t),\) \(\alpha\) of bounded variation on [a,b] and independent of r. The results obtained are applied to the problem of evaluating the sum of a power series whose terms are given numerically with moderate accuracy. The sum is approximated using values of a finite number of terms. The stability of the process is discussed. A result on the stability of product quadrature rules is also given.
Mathematics Subject Classification ID: 65B10
Mathematics Subject Classification ID: 65D32
zbMATH DE Number: 3879970
zbMATH Keywords: convergence acceleration
zbMATH Keywords: power series
zbMATH Keywords: stability
zbMATH Keywords: product quadrature rules
MaRDI profile type: Publication
cites work: Convergence acceleration from the point of view of linear programming
cites work: Convergence acceleration on a general class of power series
cites work: On Stable Calculation of Linear Functionals
cites work: Q4482959
cites work: Sequence transformations and their applications
full work available at URL: https://doi.org/10.1007/bf01934909
OpenAlex ID: W1994586541
description: scientific article; zbMATH DE number 3879970