Geodesic
Solving systems of two–sided (max, min)–linear equations
Kybernetika, Tome 46 (2010) no. 3, pp. 405-414 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A finite iteration method for solving systems of (max, min)-linear equations is presented. The systems have variables on both sides of the equations. The algorithm has polynomial complexity and may be extended to wider classes of equations with a similar structure.
A finite iteration method for solving systems of (max, min)-linear equations is presented. The systems have variables on both sides of the equations. The algorithm has polynomial complexity and may be extended to wider classes of equations with a similar structure.
Classification : 08A72, 15A06, 15A80, 15B15, 65F10, 65Y20, 90B35, 90C47
Keywords: (max, min)-linear equations; two-sided system 
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     title = {Solving systems of two{\textendash}sided (max, min){\textendash}linear equations},
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}
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Gavalec, Martin; Zimmermann, Karel. Solving systems of two–sided (max, min)–linear equations. Kybernetika, Tome 46 (2010) no. 3, pp. 405-414. http://geodesic.mathdoc.fr/item/KYB_2010_46_3_a5/

[1] Baccelli, F. L., Cohen, G., Olsder, G. J., Quadrat, J. P.: Synchronization and Linearity. An Algebra for Discrete Event Systems. Wiley, Chichester, 1992. | MR | Zbl

[2] Butkovič, P., Hegedüs, G.: An elimination method for finding all solutions of the system of linear equations over an extremal algebra. Ekonomicko–matematický obzor 20 (1984), 203–215. | MR

[3] Butkovič, P., Zimmermann, K.: A strongly polynomial algorithm for solving two-sided linear systems in max-algebra. Discrete Applied Mathematics 154 (2006), 437–446. | DOI | MR

[4] Cechlárová, K.: Efficient computation of the greatest eigenvector in fuzzy algebra. Tatra Mt. Math. Publications 12 (1997), 73–79. | MR

[5] Cechlárová, K.: Eigenvectors of interval matrices over max-plus algebra. Discrete Applied Mathematics 150 (2005), Nos. 1–3, 2–15. | DOI | MR

[6] Cuninghame-Green, R. A.: Minimax Algebra. (Lecture Notes in Economics and Mathematical Systems 166.) Springer–Verlag, Berlin 1979. | MR | Zbl

[7] Cuninghame-Green, R. A., Butkovič, P.: The equation $A \otimes x = B \otimes y$ over (max,+). Theoretical Computer Science 293 (2003), 3–12. | DOI | MR | Zbl

[8] Cuninghame-Green, R. A., Zimmermann, K.: Equation with residual functions. Comment. Math. Univ. Carolinae 42 (2001), 729–740. | MR

[9] Sanchez, E.: Resolution of eigen fuzzy sets equations. Fuzzy Sets and Systems 1 (1978), 69–74. | DOI | MR | Zbl

[10] Sanchez, E.: Inverses of fuzzy relations. Applications to possibility distributions and medical diagnosis. Fuzzy Sets and Systems 1 (1978), 75–86. | MR | Zbl

[11] Vorobjov, N. N.: Extremal algebra of positive matrices (in Russian). Datenverarbeitung und Kybernetik 3 (1967), 39–71. | MR