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Eigenproblem in extremal algebras. (English) Zbl 1135.15004

Zadnik Stirn, Lidija (ed.) et al., SOR ’07. Proceedings. The 9th international symposium on operational research in Slovenia, Nova Gorica, Slovenia, September 26–28, 2007. Ljubljana: Slovenian Society Informatika (SDI), Section for Operational Research (SOR) (ISBN 978-9-616165-25-9/pbk). 15-21 (2007).
Summary: Extremal algebra deals with extremal operations: maximum and minimum, which are used in place of operations of addition and multiplication used in the linear algebra. For a given \(n\times n\) matrix \(A\) in an extremal algebra, the eigenvalue-eigenvector problem is studied. The properties of eigenvectors and the structure of the eigenspace \({\mathcal F}(A)\), from various points of view are described. The computational complexity of the presented algorithms, for general case and also for special types of matrices, is evaluated.
For the entire collection see [Zbl 1121.90005].

MSC:

15A18 Eigenvalues, singular values, and eigenvectors
15B33 Matrices over special rings (quaternions, finite fields, etc.)
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65Y20 Complexity and performance of numerical algorithms
08A72 Fuzzy algebraic structures
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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