A singular value inequality for block matrices
type: Item
instance of: scholarly article
title: A singular value inequality for block matrices
zbMATH Open document ID: 0682.15014
DOI: 10.1016/0024-3795(89)90036-0
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
review text: The main result of this paper suggests itself in a problem arising in numerical continuation theory. Let A be an (n,n) submatrix of a nonsingular \((n+m,n+m)\) matrix M, and let S be the inverse of the Schur complement of A in M. The authors obtain upper bounds on the p \((p=\min (m,n))\) smallest singular values of A in terms of the corresponding ones in S, and vice versa.
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 4116726
zbMATH Keywords: singular value inequality
zbMATH Keywords: block matrices
zbMATH Keywords: numerical continuation theory
zbMATH Keywords: inverse
zbMATH Keywords: Schur complement
zbMATH Keywords: upper bounds
zbMATH Keywords: smallest singular values
author: Willy J. F. Govaerts
author: John D. Pryce
describes a project that uses: PITCON
MaRDI profile type: Publication
full work available at URL: 0024-3795(89)90036-0
OpenAlex ID: W1992131434
cites work: Q3833495
cites work: Q5734756
cites work: Block elimination with one refinement solves bordered linear systems accurately
cites work: Q5672034
cites work: Q3704827
cites work: Q5674306
description: scientific article; zbMATH DE number 4116726