| 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:
|
http://hdl.handle.net/10338.dmlcz/140754 |
| . |
| 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 |
| . |
