The sign-real spectral radius and cycle products

Link:

https://hdl.handle.net/11420/9441

Autor/in:

Rump, Siegfried M.

Verlag/Körperschaft:

Hamburg University of Technology

Erscheinungsjahr:

1998

Medientyp:

Text

Schlagworte:

Componentwise distances
Perron-Frobenius theory
Sign-real spectral radius
510: Mathematik

Beschreibung:

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. © 1998 Elsevier Science Inc. All rights reserved.

Beziehungen:

DOI 10.1016/S0024-3795(98)00014-7

Quellsystem:

TUHH Open Research

Interne Metadaten

Quelldatensatz: oai:tore.tuhh.de:11420/9441