Rectangular matrix Padé approximants and square matrix orthogonal polynomials
type: Item
instance of: scholarly article
title: Rectangular matrix Padé approximants and square matrix orthogonal polynomials
zbMATH Open document ID: 0884.41011
DOI: 10.1023/A:1019177316794
author: André Draux
author: Borhane Moalla
published in: Numerical Algorithms
publication date: 1998-03-17T00:00:00Z
review text: Using the method of linear functionals introduced by \textit{C. Brezinski} [Padé-type approximation and general orthogonal polynomials (1980; Zbl 0418.41012] the authors study rectangular (left) matrix Padé approximants to formal power series with \(p\times q\) matrices as coefficients. The parallel to the classical scalar case is remarkable. Existence and uniqueness can be ascertained using (generalized) Hankel determinants, recurrence relations along a diagonal in the Padé table are given, a matrix \(qd\)-algorithm is derived. Classical results are also extended to generalized square matrix orthogonal polynomials and their associated polynomials with respect to the linear functional. Finally the connection between right and left matrix Padé approximant is studied. The resuts show that the method originally introduced for the scalar case (Brezinski loc. cit.) extends in a natural way to the much more intricate situation of non-square matrix approximants.
Mathematics Subject Classification ID: 41A21
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 65D20
zbMATH DE Number: 1078342
zbMATH Keywords: rectangular matrix Padé-type approximant
zbMATH Keywords: regular matrix Padé approximant
zbMATH Keywords: matrix orthogonal polynomials
zbMATH Keywords: matrix \(qd\)-algorithm
reviewed by: Marcel G. de Bruin
MaRDI profile type: Publication
full work available at URL: a:1019177316794
OpenAlex ID: W362535484
description: scientific article; zbMATH DE number 1078342