HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Reports

Asymptotics of the Perron Eigenvalue and Eigenvector Using Max-Algebra

Abstract : We consider the asymptotics of the Perron eigenvalue and eigenvector of irreducible nonnegative matrices whose entries have a geometric dependance in a large parameter. The first term of the asymptotic expansion of these spectral elements is solution of a spectral problem in a semifield of jets, which generalizes the max-algebra. We state a «Perron-Frobenius theorem» in this semifield, which allows us to characterize the first term of this expansion in some non-singular cases. The general case involves an aggregation procedure à la Wentzell-Freidlin.
Document type :
Reports
Complete list of metadata

Cited literature [14 references]  Display  Hide  Download

https://hal.inria.fr/inria-00073240
Contributor : Rapport de Recherche Inria Connect in order to contact the contributor
Submitted on : Wednesday, May 24, 2006 - 12:18:14 PM
Last modification on : Friday, February 4, 2022 - 3:13:50 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:39:17 PM

Identifiers

  • HAL Id : inria-00073240, version 1

Collections

Citation

Marianne Akian, Ravindra Bapat, Stéphane Gaubert. Asymptotics of the Perron Eigenvalue and Eigenvector Using Max-Algebra. [Research Report] RR-3450, INRIA. 1998. ⟨inria-00073240⟩

Share

Metrics

Record views

160

Files downloads

355