The compass (star) identity for vector-valued rational interpolants
type: Item
instance of: scholarly article
title: The compass (star) identity for vector-valued rational interpolants
zbMATH Open document ID: 0888.41007
DOI: 10.1023/A:1018951020406
published in: Advances in Computational Mathematics
publication date: 1998-05-25T00:00:00Z
review text: The compass identity, also known as Wynn's five point star identity, connects five neighbouring elements in the Padé table: a central element and its four immediate neighbours in the main compass directions. Such a relation has been generalized to vector-valued rational interpolants [\textit{P. R. Graves-Morris} and \textit{C. D. Jenkins}, Vector valued rational interpolants III, Constructive Approximation 2, 263-289 (1986; Zbl 0614.41016)]. The original proof makes use of five-point relations connecting the scalar denominators and the vector-valued numerators separately. In this paper, another derivation of the latter identities is given. The proof is based on generalizations of classical Frobenius identities. Conclusions about minimality of the degrees in numerator and denominator representing the approximants and results about unattainable points are also given.
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 41A21
zbMATH DE Number: 1083927
zbMATH Keywords: rational interpolation
zbMATH Keywords: Newton-Padé approximation
author: Peter R. Graves-Morris
author: Bernhard Beckermann
reviewed by: Adhemar Bultheel
MaRDI profile type: Publication
full work available at URL: a:1018951020406
OpenAlex ID: W99616458
description: scientific article; zbMATH DE number 1083927