Paper Info
Title
Equality conditions for lower bounds on the smallest singular value of a bidiagonal matrix
Abstract
Several lower bounds have been proposed for the smallest singular value of a square matrix, such as Johnson’s bound, Brauer-type bound, Li’s bound and Ostrowski-type bound. In this paper, we focus on a bidiagonal matrix and investigate the equality conditions for these bounds. We show that the former three bounds give strict lower bounds if all the bidiagonal elements are non-zero. For the Ostrowski-type bound, we present an easily verifiable necessary and sufficient condition for the equality to hold.
Year
DOI
Venue
2008
10.1016/j.amc.2007.11.005
Applied Mathematics and Computation
Keywords
Field
DocType
Singular values,Lower bounds,Equality conditions,Bidiagonal matrix,dqds Algorithm
Mathematical optimization,Singular value,Upper and lower bounds,Mathematical analysis,Square matrix,Bidiagonal matrix,Verifiable secret sharing,Numerical analysis,Mathematics
Journal
Volume
Issue
ISSN
200
1
0096-3003
Citations 
PageRank 
References 
0
0.34
0
Authors
1
Name
Order
Citations
PageRank
Yusaku Yamamoto15220.61