Global identities in the non-normal Newton--Padé approximation table
type: Item
instance of: scholarly article
title: Global identities in the non-normal Newton--Padé approximation table
zbMATH Open document ID: 0780.41007
author: Bernhard Beckermann
author: C. Carstensen
published in: Journal of Approximation Theory
publication date: 1993-08-25T00:00:00Z
review text: The block structure in a Newton-Padé table is studied. If a vector \((z_ 0,z_ 1,\dots)\) of interpolation knots in the complex plane \(\mathbb{C}\) and a sufficiently smooth function \(f\) is given, then the Newton- Padé table is the doubly infinity array of rational functions \(r_{mn}\) of degree at most \(m\) and \(n\) that interpolate \(f\) in the points \(z_ 0,z_ 1,\dots, z_{m+n}\). (In the case that a proper interpolant does not exist, the linearized version is used.) In the paper the structure of singular blocks is investigated, identities between adjacent entries of singular blocks are presented, and in particular Cordellier's identities are generalized to the Newton-Padé table. Such identities lead to algorithms for calculating entries in a Newton-Padé table. Such identities lead to algorithms for calculating entries in a Newton-Padé table in an efficient way.
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 30E10
zbMATH DE Number: 370440
zbMATH Keywords: Newton-Padé table
zbMATH Keywords: singular blocks
reviewed by: Herbert Stahl
MaRDI profile type: Publication
full work available at URL: jath.1993.1061
OpenAlex ID: W2085852210
DOI: 10.1006/JATH.1993.1061
description: scientific article; zbMATH DE number 370440