Eigenvectors in bottleneck algebra
✍ Scribed by Katarína Cechlárová
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 574 KB
- Volume
- 175
- Category
- Article
- ISSN
- 0024-3795
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📜 SIMILAR VOLUMES
The results concerning strong regularity of matrices over bottleneck algebras are reviewed. We extend the known conditions to the discrete bounded case and modify the known algorithms for testing strong regularity.
Let a ⊕ b = max(a, b) and a ⊗ b = a + b for a, b ∈ R := R ∪ {-∞} and extend these operations to matrices and vectors as in conventional linear algebra. The following eigenvector problem has been intensively studied in the past: Given A ∈ R n×n find all x ∈ R n , x / = (-∞, . . . , -∞) T (eigenvector
We consider the eigenvalue problem in the max-plus algebra for matrices in fÀI Rg nÂn but with eigenvectors in R n . The problem is relaxed to a linear optimization (LO) problem of which the dual problem is solved by ®nding a maximal average weight circuit in the graph of the matrix. The Floyd±Warsh