Advertisement

Discrete Event Dynamic Systems

, Volume 27, Issue 1, pp 181–203 | Cite as

On a generalization of power algorithms over max-plus algebra

  • Kistosil FahimEmail author
  • Subiono
  • Jacob van der Woude
Article
  • 841 Downloads

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.

Keywords

Max-plus algebra Generalized eigenmode Power algorithm Cycle time vector 

References

  1. 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 zbMATHGoogle Scholar
  2. Braker JG, Olsder GJ (1993) The power algorithm in max algebra. Linear Algebra Appl 182:67–89MathSciNetCrossRefzbMATHGoogle Scholar
  3. 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, FranceGoogle Scholar
  4. Fahim K, Hanafi L, Subiono, Ayu F (2014) Monorail and tram scheduling which integrated surabaya using max-plus algebraGoogle Scholar
  5. Heidergott B, Olsder GJ, van der Woude JW (2006) Max plus at work. Princeton University Press, New JerseyGoogle Scholar
  6. Mufid MS, Subiono (2014) Eigenvalues and eigenvectors of latin squares in max-plus algebra. J Indones Math Soc 20(1):37–45MathSciNetzbMATHGoogle Scholar
  7. Olsder GJ (1991) Eigenvalues of dynamical min-max systems. Discrete Event Dynamical Systems 1:177–207CrossRefzbMATHGoogle Scholar
  8. Pesko S, Turek M, Turek R (2012) Max-plus algebra at road transportation. In: Proceedings of 30th international conference mathematical methods in economicsGoogle Scholar
  9. 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)
  10. 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
  11. Subiono, Shofianah N (2009) Using max-plus algebra in the flow shop scheduling. IPTEK. The Journal of Technology and Science 20(3)Google Scholar
  12. Subiono, van der Woude JW (2000) Power algorithm for (max,+)-and bipartite (m i n,m a x,+)-systems. Discrete Event Dynamical Systems 10:369–389Google Scholar
  13. Tomaskova K (2015) Max-plus algebra and its application in spreading of information. MACMESE, ISBN: 978-1-61804-117-3Google Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of MathematicsInstitut Teknologi Sepuluh NopemberSurabayaIndonesia
  2. 2.Applied Mathematics DepartmentDelft University of TechnologyDelftThe Netherlands

Personalised recommendations