Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4634723 | Applied Mathematics and Computation | 2008 | 7 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Yusaku Yamamoto,