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Computing an Eigenvector of a Monge Matrix in Max-Plus Algebra

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Abstract

The problem of finding one eigenvector of a given Monge matrix A in a max-plus algebra is considered. For a general matrix, the problem can be solved in O(n 3) time by computing one column of the corresponding metric matrix Δ(A λ), where λ is the eigenvalue of A. An algorithm is presented, which computes an eigenvector of a Monge matrix in O(n 2) time.

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Authors and Affiliations

  1. Department of Information Technologies, Faculty of Informatics and Management, University Hradec Králové, Rokitanského 62, 50003, Hradec Králové, Czech Republic

    Martin Gavalec

  2. Departments of Mathematics, Faculty of Electrical Engineering and Informatics, Technical University in Košice, B.N mcovej 32, 04200, Košice, Slovak Republic

    Ján Plavka

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  1. Martin Gavalec
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  2. Ján Plavka
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Correspondence to Martin Gavalec.

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Gavalec, M., Plavka, J. Computing an Eigenvector of a Monge Matrix in Max-Plus Algebra. Math Meth Oper Res 63, 543–551 (2006). https://doi.org/10.1007/s00186-005-0053-1

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  • DOI: https://doi.org/10.1007/s00186-005-0053-1

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