| Title:
|
Solvability of (max,+) and (min,+)-equation systems (English) |
| Author:
|
Zimmermann, Karel |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
61 |
| Issue:
|
1 |
| Year:
|
2025 |
| Pages:
|
133-140 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
max-algebraic and min-algebraic linear equation systems |
| Keyword:
|
solvability conditions |
| Keyword:
|
two-sided max-/min- algebraic linear equation systems |
| MSC:
|
15A99 |
| MSC:
|
90C31 |
| DOI:
|
10.14736/kyb-2025-1-0133 |
| . |
| Date available:
|
2025-04-07T09:45:06Z |
| Last updated:
|
2025-04-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152928 |
| . |
| Reference:
|
[1] Butkovič, P.: Max-linear Systems: Theory and Algorithms..Monographs in Mathematics, Springer Verlag 2010. Zbl 1202.15032, MR 2681232 |
| Reference:
|
[2] Cuninghame-Green, R. A.: Minimax Algebra..Lecture Notes in Economics and Mathematical Systems 166, Springer Verlag, Berlin 1979. Zbl 0739.90073, MR 0580321 |
| Reference:
|
[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. MR 2148995 |
| Reference:
|
[4] Vorobjov, N. N.: Extremal Algebra of Positive Matrices. (In Russian.).Datenverarbeitung und Kybernetik 3 (1967), 39-71. MR 0216854 |
| Reference:
|
[5] Myšková, H., Plávka, J.: The robustness of interval matrices in max-plus algebra..Linear Algebra Appl. 445 (2014), 85-102. MR 3151265, |
| Reference:
|
[6] Krivulin, N. K.: On the Solution of the two-sided vector equation..In: Tropical Algebra, Vestnik, St. Petersburg University, Mathematics 56 (2023) 2, 236-248. MR 4593654, |
| Reference:
|
[7] Cunninghame-Green, R. A., Zimmermann, K.: Equation with residual functions..CMUC 42 (2001), 729-740. MR 1883381, |
| Reference:
|
[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. |
| . |
