Contractive Laurent fractions and nested discs
type: Item
instance of: scholarly article
title: Contractive Laurent fractions and nested discs
zbMATH Open document ID: 0679.40002
DOI: 10.1016/0021-9045(89)90105-6
author: Olav Njåstad
published in: Journal of Approximation Theory
publication date: 1989-01-01T00:00:00Z
review text: A Laurent fraction is a continued fraction \(K(a_ n(z)/b_ n(z))\) where \(a_ n(z)\) and \(b_ n(z)\) are certain Laurent polynomials of the form \(p_ nz^{-1}+q_ n+r_ nz\) for constants \(p_ n\), \(q_ n\), \(r_ n\). Certain circular disks are connected with the approximants of the Laurent fraction. These disks form, under certain circumstances, a sequence of nested circles and can therefore aid in questions of convergence and error estimates. Under special conditions so called generalized approximants are shown to have very simple partial fraction decompositions. The theorems are too complicated to quote here. The proofs employ information from a number of papers by the author and/or W. B. Jones and/or W. J. Thron.
Mathematics Subject Classification ID: 40A15
zbMATH DE Number: 4113194
zbMATH Keywords: Laurent fraction
zbMATH Keywords: error estimates
reviewed by: Arne Magnus
MaRDI profile type: Publication
full work available at URL: 0021-9045(89)90105-6
OpenAlex ID: W2020975215
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description: scientific article; zbMATH DE number 4113194