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inria-00073240, version 1

Asymptotics of the Perron Eigenvalue and Eigenvector Using Max-Algebra

Marianne Akian () 1, Ravindra Bapat, Stéphane Gaubert () 1

N° RR-3450 (1998)

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.

  • 1:  META2 (INRIA Rocquencourt)
  • INRIA
  • Domain : Computer Science/Other
  • Keywords : PERRON-FROBENIUS THEOREM / MAX-ALGEBRA / PERTURBATION OF EIGENVALUES / PERTURBATION OF LINEAR OPERATORS / ASYMPTOTICS / FREIDLIN-WENTZELL THEORY / LARGE DEVIATIONS
  • Internal note : RR-3450
  • Comment : Projet META2
 
  • inria-00073240, version 1
  • http://hal.inria.fr/inria-00073240
  • oai:hal.inria.fr:inria-00073240
  • From: Rapport De Recherche Inria <>
  • Submitted on: Wednesday, 24 May 2006 12:18:14
  • Updated on: Wednesday, 18 April 2007 12:04:00