Vector Padé-type approximants and vector Padé approximants
type: Item
instance of: scholarly article
title: Vector Padé-type approximants and vector Padé approximants
zbMATH Open document ID: 0921.41007
author: K. Appert
published in: Journal of Approximation Theory
publication date: 1999-09-24T00:00:00Z
review text: The theory of scalar Padé and Padé-type approximants is generalized to the vector case. Like in \textit{A. Salam} [Adv. Comput. Math. 8, No. 3, 267-289 (1998; Zbl 0906.42013)] Clifford algebra techniques are used that differ however from those used in \textit{D. E. Roberts} [Clifford algebras and vector-valued rational forms. I: Proc. R. Soc. Lond., Ser. A 431, No. 1882, 285-300 (1990; Zbl 0745.41017); II: Numer. Algorithms 3, No. 1-4, 371-381 (1992; Zbl 0782.41022)]. The relation between both, and the link with the generalized inverse Padé approximants of \textit{P. Graves-Morris} [Vector valued interpolants I: Numer. Math. 42, 331-348 (1983; Zbl 0525.41014); II: IMA J. Numer. Anal. 4, 209-224 (1984; Zbl 0558.41019)] and \textit{P. Graves-Morris} and \textit{C. D. Jenkins} [III: Constructive Approximation 2, 263-289 (1986; Zbl 0614.41016)] is given. The derivation relies on the vector orthogonal polynomials developed by the author in the paper mentioned. Thanks to the Clifford algebra techniques direct generalizations of scalar results, including a \(qd\)-algorithm and continued fractions are obtained.
Mathematics Subject Classification ID: 41A21
zbMATH DE Number: 1286391
zbMATH Keywords: vector Padé approximant
zbMATH Keywords: vector Padé-type approximant
zbMATH Keywords: Clifford algebra
zbMATH Keywords: \(qd\)-algorithm
zbMATH Keywords: continued fraction
zbMATH Keywords: vector orthogonal polynomials
reviewed by: Adhemar Bultheel
MaRDI profile type: Publication
full work available at URL: jath.1997.3263
OpenAlex ID: W2090280625
cites work: Theory and recursive computation of 1-D matrix Pade approximants
cites work: Padé-type approximation and general orthogonal polynomials
cites work: Q3126793
cites work: Vector valued rational interpolants. I
cites work: Vector-valued Rational Interpolants II
cites work: Vector-valued, rational interpolants. III
cites work: A review of Padé methods for the acceleration of convergence of a sequence of vectors
cites work: From matrix to vector Padé approximants
cites work: Matrix representations of Clifford algebras
cites work: A note on the \(\epsilon\)-algorithm
cites work: Q5849795
cites work: Q5579608
cites work: Clifford algebras and vector-valued rational forms. I
cites work: Clifford algebras and vector-valued rational forms. II
cites work: Formal vector orthogonal polynomials
cites work: Non-commutative extrapolation algorithms
cites work: What is a vector Hankel determinant
cites work: Vector continued fractions
cites work: Continued fractions whose coefficients obey a non-commutative law of multiplication
DOI: 10.1006/JATH.1997.3263
description: scientific article; zbMATH DE number 1286391