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Almost sharp bounds for the componentwise distance to the nearest singular matrix
Publikationstyp
Journal Article
Date Issued
1997
Sprache
English
Author(s)
Institut
TORE-URI
Journal
Volume
42
Issue
2
Start Page
93
End Page
107
Citation
Linear and Multilinear Algebra 42 (2): 93-107 (1997)
Publisher DOI
Scopus ID
Publisher
Taylor & Francis
The normwise distance of a regular matrix A ∈ M (ℝ) to the nearest singular matrix is well known to be ∥A ∥ . Such a normwise distance neglects small entries in the matrix, and it does not allow for weights in a perturbation. The reciprocal ∥ |A |·E∥ of the Bauer-Skeel condition number is known to be a lower bound for the componentwise distance of A to the nearest singular matrix weighted by the nonnegative matrix E. In this paper we derive an upper bound for this componentwise distance involving the Bauer-Skeel condition number. We show that this upper bound is sharp up to a constant factor less than 3 + 2√2, independent of A and E. For finite values of n, improved constants are given as well. © 1997 OPA (Overseas Publishers Association) Amsterdam B.V. Published in The Netherlands under license by Gordon and Breach Science Publishers. n -1 -1 -1 -1
DDC Class
004: Informatik
510: Mathematik