| Title:
|
An iterative algorithm for computing the cycle mean of a Toeplitz matrix in special form (English) |
| Author:
|
Szabó, Peter |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
49 |
| Issue:
|
4 |
| Year:
|
2013 |
| Pages:
|
636-643 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper presents an iterative algorithm for computing the maximum cycle mean (or eigenvalue) of $n\times n$ triangular Toeplitz matrix in max-plus algebra. The problem is solved by an iterative algorithm which is applied to special cycles. These cycles of triangular Toeplitz matrices are characterized by sub-partitions of $n-1$. (English) |
| Keyword:
|
max-plus algebra |
| Keyword:
|
eigenvalue |
| Keyword:
|
sub-partition of an integer |
| Keyword:
|
Toeplitz matrix |
| MSC:
|
15A80 |
| MSC:
|
15B05 |
| MSC:
|
90C27 |
| . |
| Date available:
|
2013-09-17T16:33:02Z |
| Last updated:
|
2013-09-17 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143450 |
| . |
| Reference:
|
[1] Butkovič, P.: Max-linear Systems: Theory and Algorithms..Springer-Verlag, London 2010. Zbl 1202.15032, MR 2681232 |
| Reference:
|
[2] Cuninghame-Green, R. A.: Minimax Algebra..Springer-Verlag, Berlin 1979. Zbl 0739.90073, MR 0580321 |
| Reference:
|
[3] Heidergott, B., Olsder, G. J., Woude, J. van der: Max Plus at Work. Modeling and Analysis of Synchronized Systems..Princeton University Press 2004. |
| Reference:
|
[4] Heinig, G.: Not every matrix is similar to a Toeplitz matrix..Linear Algebra Appl. 332-334 (2001), 519-531. Zbl 0985.15013, MR 1839449 |
| Reference:
|
[5] Karp, R. M.: A characterization of the minimum cycle mean in a digraph..Discrete Math. 23 (1978), 309-311. Zbl 0386.05032, MR 0523080 |
| Reference:
|
[6] Landau, H. J.: Tile inverse eigenvalue problem for real symmetric Toeplitz matrices..J. Amer. Math. Soc. 7 (1994), 749-767. MR 1234570, 10.1090/S0894-0347-1994-1234570-6 |
| Reference:
|
[7] Plavka, J.: Eigenproblem for monotone and Toeplitz matrices in a max-algebra..Optimization 53 (2004), 95-101. Zbl 1079.93033, MR 2040637, 10.1080/02331930410001661497 |
| Reference:
|
[8] Szabó, P.: A short note on the weighted sub-partition mean of integers..Oper. Res. Lett. 37(5) (2009), 356-358. Zbl 1231.05017, MR 2573448, 10.1016/j.orl.2009.04.003 |
| Reference:
|
[9] Zimmermann, K.: Extremální algebra (in Czech)..Ekonomický ústav SAV, Praha 1976. |
| . |
