Displacement structure of weighted pseudoinverses
type: Item
instance of: scholarly article
title: Displacement structure of weighted pseudoinverses
zbMATH Open document ID: 1059.15013
DOI: 10.1016/S0096-3003(03)00633-7
published in: Applied Mathematics and Computation
publication date: 2004-08-06T00:00:00Z
review text: It is known that if the rank of a matrix displacement is small then fast algorithms for this matrix are available. The paper deals with the estimates for the rank of \(A^+_{M,N} V - U A^+_{M,N}\)-type displacements, that provide some extensions of known results on Sylvester and Stein UV-displacements. Here \(A^+_{M,N}\) denotes the weighted Moore-Penrose inverse of \(A\), where \(M\) and \(N\) are square Hermitian positive definite complex matrices. The above results are applied then to obtain the corresponding bounds for some generalizations of Toeplitz, Vandermonde, and Cauchy matrices.
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 2082052
zbMATH Keywords: displacement
zbMATH Keywords: weighted pseudoinverse
zbMATH Keywords: structured matrix
zbMATH Keywords: Hermitian matrix
zbMATH Keywords: Toeplitz matrix
zbMATH Keywords: Vandermonde matrix
zbMATH Keywords: rank
zbMATH Keywords: weighted Moore-Penrose inverse
zbMATH Keywords: Cauchy matrices
author: Jian-Feng Cai
author: Yimin Wei
reviewed by: Alexander Guterman
MaRDI profile type: Publication
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full work available at URL: s0096-3003(03)00633-7
OpenAlex ID: W1989196029
description: scientific article; zbMATH DE number 2082052