The practical use of the Euler transformation
type: Item
instance of: scholarly article
title: The practical use of the Euler transformation
zbMATH Open document ID: 0673.65001
DOI: 10.1007/BF01952689
author: R. E. Scraton
published in: BIT
publication date: 1989-01-01T00:00:00Z
review text: It is known that the generalized Euler transformation is one of the classical transformations of infinite series which can be used for the acceleration of convergence. If we apply this transformation to one series with rounded coefficients then its behaviour can differ from that predicted, theoretically. In this case, the author explains that it is possible to use this transformation for acceleration of convergence, but some changes are necessary in the method of choosing the optimum parameter value. This is shown with an illustrative example of a series solution of a linear differential equation.
Mathematics Subject Classification ID: 65B05
Mathematics Subject Classification ID: 40G05
zbMATH DE Number: 4102364
zbMATH Keywords: Euler transformation
zbMATH Keywords: acceleration of convergence
reviewed by: Antonio López-Carmona
describes a project that uses: Algorithm 38
MaRDI profile type: Publication
cites work: Convergence acceleration on a general class of power series
cites work: Algorithm 38. Two computer codes for convergence acceleration
cites work: On the stability of a class of convergence acceleration methods for power series
cites work: Q5562171
cites work: A note on the generalised Euler transformation
full work available at URL: https://doi.org/10.1007/bf01952689
OpenAlex ID: W2019147268
description: scientific article; zbMATH DE number 4102364