Computing matrix period in max-min algebra
โ Scribed by Martin Gavalec
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 527 KB
- Volume
- 75
- Category
- Article
- ISSN
- 0166-218X
No coin nor oath required. For personal study only.
โฆ Synopsis
Periodicity of matrix powers in max-min algebra is studied. The period of a matrix A is shown to be the least common multiple of the periods of at most n non-trivial strongly connected components in some threshold digraphs of A. An O(n3) algorithm for computing the period is described.
๐ SIMILAR VOLUMES
The problem of the strong regularity of a square matrix in a general max-min algebra is considered and a necessary and sufficient condition using the trapezoidal property is described. The results are valid without any restrictions on the underlying max-min algebra, concerning the density, or the bo
A speed-up of a known O(n 3 ) algorithm computing the period of a periodic orbit in max-min algebra is presented. If the critical components (or the transitive closure A + ) of the transition matrix A are known, the computational complexity of the algorithm is O(n 2 ). This is achieved by using only