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Optimal scaling for p-norms and componentwise distance to singularity
Publikationstyp
Journal Article
Date Issued
2003-01-01
Sprache
English
Author(s)
Institut
TORE-URI
Volume
23
Issue
1
Start Page
1
End Page
9
Citation
IMA Journal of Numerical Analysis 1 (23): 1-9 (2003-01-01)
Publisher DOI
Scopus ID
Publisher
Oxford Univ. Press
We give lower and upper bounds for the optimal p-norm condition number achievable by two-sided diagonal scalings. There are no assumptions on the irreducibility of certain matrices. The bounds are shown to be optimal for the 2-norm. For the 1-norm and inf-norm the (known) exact value of the optimal condition number is confirmed. We give means how to calculate the minimizing diagonal matrices. Furthermore, a class of new lower bounds for the componentwise distance to the nearest singular matrix is given. They are shown to be superior to existing ones.
Subjects
Componentwise distance to singularity
Condition number, p-norm
Interval matrix
Optimal scaling
Strongly regular
DDC Class
004: Informatik
510: Mathematik
600: Technik