Asymptotics of the Perron eigenvalue and eigenvector using max-algebra;Asymptotique de la valeur propre et du vecteur propre de Perron via l'algèbre max-plus

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 327, Issue 11, 1998, Pages 927-932

  Akian, Marianne ^a   Bapat, Ravindra ^b   Gaubert, Stéphane ^a  

^a INRIA   (France)

^b INDIAN STATISTICAL INSTITUTE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032325525     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0764-4442(99)80137-2     Document Type: Article

References (15)

1. [1] Akian M., Bapat R.B., Gaubert S., Asymptotics of the Perron eigenvalue and eigenvector, (1998) (in preparation).
2. [2] Baccelli F., Cohen G., Olsder G.J., Quadrat J.P., Synchronization and Linearity, Wiley, 1992.
3. [3] Baxter R.J., Exactly solved models in Statistical Mechanics, Academic Press, New York, 1982.
4. [4] Berman A., Plemmons R.J., Nonnegative matrices in the mathematical sciences, Academic Press, 1979.
5. [5] Chou W., Griffiths R.B., Ground states of one dimensional systems using effective potentials, Phys. Rev. B 34 (1986) 6219-34.
6. [6] Cuninghame-Green R.A., Minimax algebra and applications, Advances in Imaging and Electron Physics 90 (1995).
7. [7] Dobrokhotov S.Yu., Kolokoltsov V.N., Maslov V.P., Quantization of the Bellman equation, exponential asymptotics and tunneling, In: V.P. Maslov, S.N. Samborskiǐ (Eds.), Idempotent analysis, Vol. 13 of Adv. in Sov. Math. AMS, RI, 1992.
8. [8] Finkelstein A.V., Roytberg M.A., Computation of biopolymers: a general approach to different problems, BioSystems 30 (1993) 1-20.
9. [9] Freidlin M.I., Wentzell A.D., Random Perturbations of Dynamical Systems, Springer, 1984.
10. [10] Friedland S., Limit eigenvalues of nonnegatives matrices, Linear Alg. and Appl. 74 (1986) 173-178.
11. [11] Gaubert S., Plus M., Methods and applications of (max,+) linear algebra, In: R. Reischuk, M. Morvan (Eds.), STACS'97, LNCS 1200, Lübeck, Springer, 1997.
12. [12] Gondran M., Minoux M., Valeurs propres et vecteurs propres dans les dioïdes et leur interprétation en théorie des graphes, EDF, Bulletin de la Direction des Études et Recherches, Série C, Mathématiques, Informatique 2 (1977) 25-41.
13. [13] Gondran M., Minoux M., Graphes et algorithmes, Eyrolles, Paris, 1979. Engl. transl. Graphs and Algorithms, Wiley, 1984.
14. [13] Gondran M., Minoux M., Graphes et algorithmes, Eyrolles, Paris, 1979. Engl. transl. Graphs and Algorithms, Wiley, 1984.
15. [14] Hardy G.H., Riesz M., The general theory of Dirichlet's series, Cambridge University Press, 1915.