The sign-real spectral radius and cycle products

Publikationstyp
Journal Article
Date Issued
1998-11-02
Sprache
English
Author(s)
Rump, Siegfried M.  orcid-logo
Institut
Zuverlässiges Rechnen E-19  
TORE-URI
http://hdl.handle.net/11420/9441
Journal
Linear algebra and its applications  
Volume
279
Issue
1-3
Start Page
177
End Page
180
Citation
Linear Algebra and Its Applications 279 (1-3): 177-180 (1998)
Publisher DOI
10.1016/S0024-3795(98)00014-7
Scopus ID
2-s2.0-0042595949
Publisher
American Elsevier Publ.
The extension of the Perron-Frobenius theory to real matrices without sign restriction uses the sign-real spectral radius as the generalization of the Perron root. The theory was used to extend and solve the conjecture in the affirmative that an ill-conditioned matrix is nearby a singular matrix also in the componentwise sense. The proof estimates the ratio between the sign-real spectral radius and the maximum geometric mean of a cycle product. In this note we discuss bounds for this ratio including a counterexample to a conjecture about this ratio.
Subjects
Componentwise distances
Perron-Frobenius theory
Sign-real spectral radius
DDC Class
510: Mathematik