Generalized Cauchy-Vandermonde matrices
type: Item
instance of: scholarly article
title: Generalized Cauchy-Vandermonde matrices
zbMATH Open document ID: 0913.15016
DOI: 10.1016/S0024-3795(97)00034-7
author: G. Heinig
published in: Linear Algebra and its Applications
publication date: 1999-05-31T00:00:00Z
review text: This paper thoroughly deals with matrices of the form \([C V]\) consisting of a generalized Cauchy matrix \(C\) and a generalized Vandermonde matrix \(V.\) The displacement structure of these generalized Cauchy-Vandermonde (CV) matrices is used in order to obtain formulas for the inverse of such a matrix involving solutions of the so-called fundamental equations. Linear systems of equations with a CV coefficient matrix may be interpreted as tangential interpolation problems. This leads to the concept of left and right fundamental matrices for (arbitrary) nonsingular CV matrices. A careful discussion of recursions for the fundamental matrices gives rise to fast algorithms (of Levinson and Schur types) for evaluating the inverse of a CV matrix.
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 65F05
zbMATH DE Number: 1109494
zbMATH Keywords: Cauchy matrices
zbMATH Keywords: Vandermonde matrices
zbMATH Keywords: inversion formulas
zbMATH Keywords: tangential interpolation problems
zbMATH Keywords: generalized Cauchy-Vandermonde matrices
zbMATH Keywords: fundamental matrices
zbMATH Keywords: fast algorithms
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1109494