Skip to main content
Log in

On a generalization of power algorithms over max-plus algebra

  • Published:
Discrete Event Dynamic Systems Aims and scope Submit manuscript

Abstract

In this paper we discuss a generalization of power algorithms over max-plus algebra. We are interested in finding such a generalization starting from various existing power algorithms. The resulting algorithm can be used to determine the so-called generalized eigenmode of any square regular matrix over max-plus algebra. In particular, the algorithm can be applied in the case of regular reducible matrices in which the existing power algorithms can not be used to compute eigenvalues and corresponding eigenvectors.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

References

  • Baccelli F, Cohen G, Olsder GJ, Quadrat JP (1992) Synchronization and linearity. An algebra for discrete event systems. Wiley, London, p 489. web version can be downloaded https://www.rocq.inria.fr/metalau/cohen/documents/BCOQ-book.pdf

    MATH  Google Scholar 

  • Braker JG, Olsder GJ (1993) The power algorithm in max algebra. Linear Algebra Appl 182:67–89

    Article  MathSciNet  MATH  Google Scholar 

  • Cochet-Terrasson J, Cohen G, Gaubert S, Mc Gettrick M, Quadrat JP (1998) Numerical computation of spectral elements in (max,+) algebra. In: IFAC Conference on System Structure and Control. Nantes, France

  • Fahim K, Hanafi L, Subiono, Ayu F (2014) Monorail and tram scheduling which integrated surabaya using max-plus algebra

    Google Scholar 

  • Heidergott B, Olsder GJ, van der Woude JW (2006) Max plus at work. Princeton University Press, New Jersey

  • Mufid MS, Subiono (2014) Eigenvalues and eigenvectors of latin squares in max-plus algebra. J Indones Math Soc 20(1):37–45

    MathSciNet  MATH  Google Scholar 

  • Olsder GJ (1991) Eigenvalues of dynamical min-max systems. Discrete Event Dynamical Systems 1:177–207

    Article  MATH  Google Scholar 

  • Pesko S, Turek M, Turek R (2012) Max-plus algebra at road transportation. In: Proceedings of 30th international conference mathematical methods in economics

  • Subiono, Fahim K (2016) On computing supply chain scheduling using max-plus algebra. Applied Mathematical Sciences 10(10):477–486. doi:10.12988/ams.2016.618. ISSN 1312-885X (print), ISSN 1314-7552 (online)

  • Subiono, Mufid MS, Adzkiya D (2014) Eigenproblems of latin squares in bipartite (min, max,+)-systems. Discrete Event Dynamic Systems. doi:10.1007/s10626-014-0204-8. Online ISSN 1573-7594, Springer

  • Subiono, Shofianah N (2009) Using max-plus algebra in the flow shop scheduling. IPTEK. The Journal of Technology and Science 20(3)

  • Subiono, van der Woude JW (2000) Power algorithm for (max,+)-and bipartite (m i n,m a x,+)-systems. Discrete Event Dynamical Systems 10:369–389

  • Tomaskova K (2015) Max-plus algebra and its application in spreading of information. MACMESE, ISBN: 978-1-61804-117-3

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kistosil Fahim.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fahim, K., Subiono & van der Woude, J. On a generalization of power algorithms over max-plus algebra. Discrete Event Dyn Syst 27, 181–203 (2017). https://doi.org/10.1007/s10626-016-0235-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10626-016-0235-4

Keywords

Navigation