zbMATH — the first resource for mathematics

Eigenvectors in Bottleneck algebra. (English) Zbl 0756.15014
The paper deals with a characterization of the eigenvectors in terms of the associated graph and with an alternative way of computing them. Upper and lower bounds for all eigenvectors are given. The approach is illustrated by several numerical examples.
Reviewer: M.Voicu (Iaşi)

15A18 Eigenvalues, singular values, and eigenvectors
15A30 Algebraic systems of matrices
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
Full Text: DOI
[1] Butkovič, P.; Cechlárová, K.; Szabó, P., Strong linear independence in bottleneck algebra, Linear algebra appl., 94, 133-155, (1987) · Zbl 0629.90093
[2] Cuninghame-Green, R.A., Process synchronization in a steelworks, a problem of feasibility, (), 323-328
[3] Cuninghame-Green, R.A., Minimax algebra, () · Zbl 0498.90084
[4] Gondran, M., Valeurs propres et vecteurs propres en classification hierarchique, RAIRO inform. théor., 10, 3, 39-46, (Mar. 1976)
[5] Gondran, M.; Minoux, M., Valeurs propres et vecteurs propres en théorie des graphes, (), 181-183 · Zbl 0414.15011
[6] Vorobjev, N.N., Ekstremal’naya algebra polozihitel’nykh matrits, Elektron. informationsverarbeitung und kybernetik, 3, 39-71, (1967), (in Russian)
[7] Vorobjev, N.N., Ekstremal’naya algebra neotritsatel’nykh matrits, Elektron. informationsverarbeitung und kybernetik, 6, 303-312, (1970), (in Russian)
[8] Zimmermann, U., Linear and combinatorial optimization in ordered algebraic structures, () · Zbl 0466.90045
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.