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Discrete max-plus spectral theory | | Marianne Akian
; Stephane Gaubert
; Cormac Walsh
; | | Date: |
12 May 2004 | | Journal: | Appears in "Idempotent Mathematics and Mathematical Physics", G.L. Litvinov and V.P. Maslov, Eds, vol. 377 of Contemporary Mathematics, pp. 53--77, AMS, 2005. | | Subject: | Spectral Theory; Optimization and Control MSC-class: 47J10 (primary) 49L20, 15A48 (secondary) | math.SP math.OC | | Abstract: | We develop a max-plus spectral theory for infinite matrices. We introduce recurrence and tightness conditions, under which many results of the finite dimensional theory, concerning the representation of eigenvectors and the asymptotic behavior of powers of matrices, carry over. We also announce more general representation results for eigenvectors, which are obtained by introducing a max-plus analogue of the Martin boundary. | | Source: | arXiv, math.SP/0405225 | | Services: | Forum | Review | PDF | Favorites | |
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