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Asymptotics of the Perron eigenvalue and eigenvector using max-algebra

✍ Scribed by Marianne Akian; Ravindra Bapat; Stéphane Gaubert

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
484 KB
Volume
327
Category
Article
ISSN
0764-4442

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✦ Synopsis

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 a la Wentzell-Freidlin.

0 AcadCmie des Sciences/Elsevier, Paris Asymptotique de la valeur propre et du vecteur propre de Perron via l'aighbre max-plus

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