Inversion of a block Löwner matrix
type: Item
instance of: scholarly article
title: Inversion of a block Löwner matrix
zbMATH Open document ID: 0861.15003
DOI: 10.1016/0377-0427(95)00037-2
author: Marc van Barel
author: Zdeněk Vavřín
published in: Journal of Computational and Applied Mathematics
publication date: 1996-10-13T00:00:00Z
review text: Given a block Löwner matrix \[ L= \bigl((y_i-z_j)^{-1} (C_i-D_j) \bigr)_{{i= 0, \dots, m-1 \atop j = 0, \dots, n-1}}, \] where \(C_i\) and \(D_j\) are \(p \times q\) blocks with \(mp = nq\), and \(y_i,z_j \in F\) and \(\{y_0, \dots, y_{m-1}\} \cap \{z_0, \dots, z_{n-1}\}= \emptyset\), one uses the method of UV-reduction for Toeplitz-like operators and derives a simple inversion formula for \(L\). Connections with matrix rational and tangential interpolations are given and the properties of the parameters of inversion formula are examined. Finally some hints about efficient computation are given, matrix continued fraction representations are considered and the (un)attainability or (in)accessibility of interpolation points are examined.
reviewed by: Mihail Voicu
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 65F05
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 908416
zbMATH Keywords: block Löwner matrix
zbMATH Keywords: method of UV-reduction
zbMATH Keywords: Toeplitz-like operators
zbMATH Keywords: inversion formula
zbMATH Keywords: matrix rational and tangential interpolations
zbMATH Keywords: matrix continued fraction representations
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00037-2
OpenAlex ID: W2047240091
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description: scientific article; zbMATH DE number 908416