Scaling and structural condition numbers
type: Item
instance of: scholarly article
title: Scaling and structural condition numbers
zbMATH Open document ID: 0891.15003
DOI: 10.1016/S0024-3795(96)00531-9
author: Arnold Neumaier
published in: Linear Algebra and its Applications
publication date: 1997-09-29T00:00:00Z
review text: Structurally singular matrices are those whose zero patterns determine whether or not they are singular. For other matrices, the structural condition number is the ratio of the maximum absolute value of an entry to the supremum of \(\delta\) such that if we replace any entry smaller than that with zero, we get a structurally nonsingular matrix. The author characterizes the structural condition number in terms of submatrices, gets an upper bound on the structural condition number of doubly stochastic matrices, and obtains a condition for optimal scaling of symmetric matrices.
Mathematics Subject Classification ID: 15A12
Mathematics Subject Classification ID: 15B51
zbMATH DE Number: 1067948
zbMATH Keywords: structurally singular matrices
zbMATH Keywords: structural condition number
zbMATH Keywords: doubly stochastic matrices
zbMATH Keywords: optimal scaling
zbMATH Keywords: symmetric matrices
reviewed by: Ki Hang Kim
describes a project that uses: Algorithm 548
MaRDI profile type: Publication
cites work: Assignment and matching problems: solution methods with FORTRAN-programs. In cooperation with T. Bönniger and G. Katzakidis
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Wikidata QID: Q127972171
description: scientific article; zbMATH DE number 1067948