On the asymptotic behaviour of continued fractions
type: Item
instance of: scholarly article
title: On the asymptotic behaviour of continued fractions
zbMATH Open document ID: 0659.40001
DOI: 10.1016/0168-9274(83)90003-X
author: Claude Brezinski
published in: Applied Numerical Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Let \(C_ n\) be the convergents of the continued fraction \[ b_ 0+\frac{a_ 1}{1}+\frac{a_ 2}{1-a_ 2}+\frac{a_ 3}{1-a_ 3}+.... \] Then the right-hand side of \(a_ n=-\Delta C_{n-1}/\Delta C_{n- 2}\) has a limit iff the continued fraction is limit periodic. The corresponding identity for suitable contractions of the continued fraction can be used for limit k-periodic continued fractions. Convergence acceleration using both familiar techniques for sequences and modifications of the continued fraction are discussed.
Mathematics Subject Classification ID: 40A15
Mathematics Subject Classification ID: 41A20
zbMATH DE Number: 4077916
zbMATH Keywords: Convergence acceleration
reviewed by: Johan Karlsson
MaRDI profile type: Publication
cites work: The linear convergence of limit periodic continued fractions
cites work: Q4040286
cites work: On a class of nonlinear transformations and their applications to the evaluation of infinite series
cites work: Acceleration of limit periodic continued fractions by the \(T_{+M}\) transformation
cites work: Convergence acceleration of limit k-periodic continued fractions
full work available at URL: 0168-9274(83)90003-x
OpenAlex ID: W1991215354
description: scientific article; zbMATH DE number 4077916