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Power Algorithms for (max,+)- and Bipartite (min,max,+)-Systems

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Abstract

In this paper we consider(max,+)-systems and bipartite (min,max,+)-systems.We present so-called power algorithms that under some mild conditionson the structure of the systems determine eigenvalues and correspondingeigenvectors in an iterative way. We present simple proofs forour algorithms and we illustrate our algorithms by means of someexamples also clarifying the difference with existing power algorithms.

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References

  • Baccelli, F., Cohen, G., Olsder, G. J., and Quadrat, J. P. 1992. Synchronization and Linearity. Wiley.

  • Braker, J. G., and Olsder, G. J. 1993. The power algorithm in max algebra. Linear Algebra and its Applications 182: 67-89.

    Google Scholar 

  • Cochet-Terrasson, J., Cohen, G., Gaubert, S., Mc Gettrick, M., Quadrat, J. P. 1998. Numerical computation of spectral elements in max-plus algebra. Preprints of the IFAC conference on System Structure and Control, Nantes, France, July 8-10, pp. 699-706.

  • Gaubert, S. 1992. Théorie linéaire de systèms dans les dioïdes. Thesis, École des Mines de Paris, Paris.

    Google Scholar 

  • Gaubert, S., and Gunawardena, J. 1998. The duality theorem for min-max functions. C. R. Acad. Sci. Paris, t. 326, Série I, pp. 43-48.

    Google Scholar 

  • Gunawardena, J. 1994a. Min-max functions. Discrete Event Dynamic Systems 4: 377-407.

    Google Scholar 

  • Gunawardena, J. 1994b. Cycle times and fixed points of min-max functions. 11th International Conference on Analysis and Optimization of Systems. G. Cohen and J.-P. Quadrat, eds., Springer LNCIS 199, pp. 266-272.

  • Gunawardena, J., and Keane, M. 1995. On the existence of cycle times for some nonexpansive maps. Technical Report HPL-BRIMS-95-003, Hewlett-Packard labs.

  • Karp, R. M. 1978. A characterization of the minimum cycle mean in a digraph. Discrete Mathematics 23: 309-311.

    Google Scholar 

  • Olsder, G. J. 1991. Eigenvalues of dynamic max-min systems. Discrete Event Dynamic Systems 1: 177-207.

    Google Scholar 

  • Olsder,G. J., and Perennes, S. Iteration of Min-Max-Plus functions. Working paper available atwww-sop.inria.fr /sloop/personnel/Stephane.Perennes/biblio.html.

  • Subiono, Olsder, G. J. 1997. On bipartite min-max-plus systems. CD-ROM of Proceedings of the European Control Conference (ECC97), Brussels, Belgium, July 1-4, paper in session Th-E-K4.

  • van der Woude, J. W., Subiono. 1998. Conditions for the structural existence of an eigenvalue of a bipartite min, max, +)-system. TWI report 98-47, Faculty of Technical Mathematics and Informatics. Also submitted for publication in the special issue of Theoretical Computer Science on max-plus algebra.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematics and Science, Sepuluh Nopember Institute of Technology of Surabaya, Indonesia

    Subiono

  2. Subfaculty of Technical Mathematics and Informatics, Faculty of Information Technology and Systems, Delft University of Technology, Delft, the Netherlands

    Jacob van der Woude

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  1. Subiono
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  2. Jacob van der Woude
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Subiono, van der Woude, J. Power Algorithms for (max,+)- and Bipartite (min,max,+)-Systems. Discrete Event Dynamic Systems 10, 369–389 (2000). https://doi.org/10.1023/A:1008315821604

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