A unified approach to Loewner and Hankel matrices
type: Item
instance of: scholarly article
title: A unified approach to Loewner and Hankel matrices
zbMATH Open document ID: 0712.15023
DOI: 10.1016/0024-3795(91)90011-K
author: Zdeněk Vavřín
published in: Linear Algebra and its Applications
publication date: 1991-01-01T00:00:00Z
review text: The elements of Loewner matrices have the form \[ (c_ i-d_ j)/(y_ i-z_ j) \] and are associated with the theory of interpolation at simple points by rational functions. In order to deal with interpolation of both function and derivatives a more general type of matrix has to be defined; this includes the standard Loewner matrix at one extreme and Hankel matrices at the other (when all the data is at one point). The paper contains the study of these matrices and the associated interpolation problem, and includes characterization of nonsolvable cases by means of rank properties of the Loewner matrix. In order to simplify the presentation of the rather complicated material the paper is in three parts. One for the presentation of definitions and theorems, the next for appropriate proofs and the final one contains examples to illustrate the theory.
reviewed by: D. Kershaw
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 4171129
zbMATH Keywords: Loewner matrices
zbMATH Keywords: interpolation
zbMATH Keywords: rational functions
zbMATH Keywords: Hankel matrices
MaRDI profile type: Publication
cites work: On the Scalar Rational Interpolation Problem
cites work: Rational interpolation and the Euclidean algorithm
cites work: Q3921475
cites work: Q5666975
cites work: Q4405419
cites work: Hankel and Loewner matrices
cites work: Quasidirect decompositions of Hankel and Toeplitz matrices
cites work: Q3699845
cites work: On the partial realization problem
cites work: Algebraic methods for Toeplitz-like matrices and operators
cites work: Q4044730
cites work: Inverses of Löwner matrices
cites work: Multiplication of diagonal transforms of Loewner matrices
description: scientific article; zbMATH DE number 4171129