Solvability of (max,+) and (min,+)-equation systems

Karel Zimmermann

Kybernetika (2025)

  • Issue: 1, page 133-140
  • ISSN: 0023-5954

Abstract

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Properties of (max,+)-linear and (min,+)-linear equation systems are used to study solvability of the systems. Solvability conditions of the systems are investigated. Both one-sided and two-sided systems are studied. Solvability of one class of (max,+)-nonlinear problems will be investigated. Small numerical examples illustrate the theoretical results.

How to cite

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Zimmermann, Karel. "Solvability of (max,+) and (min,+)-equation systems." Kybernetika (2025): 133-140. <http://eudml.org/doc/299937>.

@article{Zimmermann2025,
abstract = {Properties of (max,+)-linear and (min,+)-linear equation systems are used to study solvability of the systems. Solvability conditions of the systems are investigated. Both one-sided and two-sided systems are studied. Solvability of one class of (max,+)-nonlinear problems will be investigated. Small numerical examples illustrate the theoretical results.},
author = {Zimmermann, Karel},
journal = {Kybernetika},
keywords = {max-algebraic and min-algebraic linear equation systems; solvability conditions; two-sided max-/min- algebraic linear equation systems},
language = {eng},
number = {1},
pages = {133-140},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Solvability of (max,+) and (min,+)-equation systems},
url = {http://eudml.org/doc/299937},
year = {2025},
}

TY - JOUR
AU - Zimmermann, Karel
TI - Solvability of (max,+) and (min,+)-equation systems
JO - Kybernetika
PY - 2025
PB - Institute of Information Theory and Automation AS CR
IS - 1
SP - 133
EP - 140
AB - Properties of (max,+)-linear and (min,+)-linear equation systems are used to study solvability of the systems. Solvability conditions of the systems are investigated. Both one-sided and two-sided systems are studied. Solvability of one class of (max,+)-nonlinear problems will be investigated. Small numerical examples illustrate the theoretical results.
LA - eng
KW - max-algebraic and min-algebraic linear equation systems; solvability conditions; two-sided max-/min- algebraic linear equation systems
UR - http://eudml.org/doc/299937
ER -

References

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  1. Butkovič, P., Max-linear Systems: Theory and Algorithms., Monographs in Mathematics, Springer Verlag 2010. Zbl1202.15032MR2681232
  2. Cuninghame-Green, R. A., Minimax Algebra., Lecture Notes in Economics and Mathematical Systems 166, Springer Verlag, Berlin 1979. Zbl0739.90073MR0580321
  3. Litvinov, G. L., Maslov, V. P., (eds.), S. N. Sergeev, Idempotent and Tropical Mathematics and Problems of Mathematical Physics, vol. I., Independent University Moscow, 2007. MR2148995
  4. Vorobjov, N. N., Extremal Algebra of Positive Matrices. (In Russian.), Datenverarbeitung und Kybernetik 3 (1967), 39-71. MR0216854
  5. Myšková, H., Plávka, J., , Linear Algebra Appl. 445 (2014), 85-102. MR3151265DOI
  6. Krivulin, N. K., , In: Tropical Algebra, Vestnik, St. Petersburg University, Mathematics 56 (2023) 2, 236-248. MR4593654DOI
  7. Cunninghame-Green, R. A., Zimmermann, K., , CMUC 42 (2001), 729-740. MR1883381DOI
  8. Aminu, A., On the solvability of homogeneous two-sided systems in max-algebra., Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132 Volume 16, 2010, Number 2, pp. 5-15. 

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