Displacement structure of pseudoinverses
type: Item
instance of: scholarly article
title: Displacement structure of pseudoinverses
zbMATH Open document ID: 0796.15007
DOI: 10.1016/0024-3795(94)90506-1
author: G. Heinig
author: Frank Hellinger
published in: Linear Algebra and its Applications
publication date: 1994-10-10T00:00:00Z
review text: A matrix or linear operator \(A\) possesses a \(UV\)-displacement structure if \(\text{rank} (AU-VA)\) is small compared with the rank of \(A\). This paper gives estimates for the displacement rank of the pseudoinverse \(A^ \dag\) of \(A\). The general results are applied to close-to-Toeplitz, close-to-Vandermonde, generalized Cauchy matrices, Bézoutians, Toeplitz and Hankel operators, singular integral operators, and integral operators with displacement kernel.
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 45P05
zbMATH DE Number: 553978
zbMATH Keywords: generalized inverse
zbMATH Keywords: Cauchy matrix
zbMATH Keywords: Toeplitz matrix
zbMATH Keywords: Vandermonde matrix
zbMATH Keywords: Hankel matrix
zbMATH Keywords: displacement structure
zbMATH Keywords: Bézout operator
zbMATH Keywords: Toeplitz operator
zbMATH Keywords: Hankel operator
zbMATH Keywords: displacement rank
zbMATH Keywords: pseudoinverse
zbMATH Keywords: singular integral operators
zbMATH Keywords: integral operators with displacement kernel
reviewed by: Stephen L. Campbell
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)90506-1
OpenAlex ID: W2078303291
cites work: Q4773298
cites work: Q4061081
cites work: Displacement structure for Hankel, Vandermonde, and related (derived) matrices
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cites work: Moore–Penrose Inversion of Square Toeplitz Matrices
cites work: Algebraic methods for Toeplitz-like matrices and operators
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cites work: Displacement ranks of matrices and linear equations
cites work: Complexity of Computations with Matrices and Polynomials
cites work: Q5645536
description: scientific article; zbMATH DE number 553978