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Title: Monotone interval eigenproblem in max–min algebra (English)
Author: Gavalec, Martin
Author: Plavka, Ján
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 46
Issue: 3
Year: 2010
Pages: 387-396
Summary lang: English
Category: math
Summary: The interval eigenproblem in max-min algebra is studied. A classification of interval eigenvectors is introduced and six types of interval eigenvectors are described. Characterization of all six types is given for the case of strictly increasing eigenvectors and Hasse diagram of relations between the types is presented. (English)
Keyword: (max, min) eigenvector
Keyword: interval coefficients
MSC: 08A72
MSC: 15A18
MSC: 15A80
MSC: 65G30
MSC: 90B35
MSC: 90C47
idZBL: Zbl 1202.15013
idMR: MR2676076
Date available: 2010-09-13T16:47:49Z
Last updated: 2013-09-21
Stable URL:
Reference: [1] Cechlárová, K.: Eigenvectors in bottleneck algebra.Lin. Algebra Appl. 175 (1992), 63–73. MR 1179341, 10.1016/0024-3795(92)90302-Q
Reference: [2] Cechlárová, K.: Solutions of interval linear systems in $(\operatorname{max},+)$-algebra.In: Proc. 6th Internat. Symposium on Operational Research, Preddvor, Slovenia 2001, pp. 321–326.
Reference: [3] Cechlárová, K., Cuninghame-Green, R. A.: Interval systems of max-separable linear equations.Lin. Algebra Appl. 340 (2002), 215–224. MR 1869429, 10.1016/S0024-3795(01)00405-0
Reference: [4] Cuninghame-Green, R. A.: Minimax Algebra.(Lecture Notes in Economics and Mathematical Systems 166.) Springer–Verlag, Berlin 1979. Zbl 0739.90073, MR 0580321
Reference: [5] Fiedler, M., Nedoma, J., Ramík, J., Rohn, J., Zimmermann, K.: Linear Optimization Problems with Inexact Data.Springer–Verlag, Berlin 2006. MR 2218777
Reference: [6] Gavalec, M.: Monotone eigenspace structure in max-min algebra.Lin. Algebra Appl. 345 (2002), 149–167. Zbl 0994.15010, MR 1883271, 10.1016/S0024-3795(01)00488-8
Reference: [7] Gavalec, M., Zimmermann, K.: Classification of solutions to systems of two-sided equations with interval coefficients.Internat. J. Pure Applied Math. 45 (2008), 533–542. Zbl 1154.65036, MR 2426231
Reference: [8] Rohn, J.: Systems of linear interval equations.Lin. Algebra Appl. 126 (1989), 39–78. Zbl 1061.15003, MR 1040771, 10.1016/0024-3795(89)90004-9


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