Geodesic
An iterative algorithm for computing the cycle mean of a Toeplitz matrix in special form
Kybernetika, Tome 49 (2013) no. 4, pp. 636-643 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 $n-1$.
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 $n-1$.
Classification : 15A80, 15B05, 90C27
Keywords: max-plus algebra; eigenvalue; sub-partition of an integer; Toeplitz matrix 
@article{KYB_2013_49_4_a8,
     author = {Szab\'o, Peter},
     title = {An iterative algorithm for computing the cycle mean of a {Toeplitz} matrix in special form},
     journal = {Kybernetika},
     pages = {636--643},
     year = {2013},
     volume = {49},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2013_49_4_a8/}
}
TY  - JOUR
AU  - Szabó, Peter
TI  - An iterative algorithm for computing the cycle mean of a Toeplitz matrix in special form
JO  - Kybernetika
PY  - 2013
SP  - 636
EP  - 643
VL  - 49
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/KYB_2013_49_4_a8/
LA  - en
ID  - KYB_2013_49_4_a8
ER  - 
%0 Journal Article
%A Szabó, Peter
%T An iterative algorithm for computing the cycle mean of a Toeplitz matrix in special form
%J Kybernetika
%D 2013
%P 636-643
%V 49
%N 4
%U http://geodesic.mathdoc.fr/item/KYB_2013_49_4_a8/
%G en
%F KYB_2013_49_4_a8
Szabó, Peter. An iterative algorithm for computing the cycle mean of a Toeplitz matrix in special form. Kybernetika, Tome 49 (2013) no. 4, pp. 636-643. http://geodesic.mathdoc.fr/item/KYB_2013_49_4_a8/

[1] Butkovič, P.: Max-linear Systems: Theory and Algorithms. Springer-Verlag, London 2010. | MR | Zbl

[2] Cuninghame-Green, R. A.: Minimax Algebra. Springer-Verlag, Berlin 1979. | MR | Zbl

[3] Heidergott, B., Olsder, G. J., Woude, J. van der: Max Plus at Work. Modeling and Analysis of Synchronized Systems. Princeton University Press 2004.

[4] Heinig, G.: Not every matrix is similar to a Toeplitz matrix. Linear Algebra Appl. 332-334 (2001), 519-531. | MR | Zbl

[5] Karp, R. M.: A characterization of the minimum cycle mean in a digraph. Discrete Math. 23 (1978), 309-311. | MR | Zbl

[6] Landau, H. J.: Tile inverse eigenvalue problem for real symmetric Toeplitz matrices. J. Amer. Math. Soc. 7 (1994), 749-767. | DOI | MR

[7] Plavka, J.: Eigenproblem for monotone and Toeplitz matrices in a max-algebra. Optimization 53 (2004), 95-101. | DOI | MR | Zbl

[8] Szabó, P.: A short note on the weighted sub-partition mean of integers. Oper. Res. Lett. 37(5) (2009), 356-358. | DOI | MR | Zbl

[9] Zimmermann, K.: Extremální algebra (in Czech). Ekonomický ústav SAV, Praha 1976.