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doi:10.1016/j.dam.2005.02.017 
Copyright © 2005 Elsevier B.V. All rights reserved.
ℓ-Parametric eigenproblem in max-algebra
Ján Plavka
Received 23 September 2003;
revised 7 October 2004;
accepted 4 February 2005.
Available online 25 May 2005.
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Abstract
Denote a
b=max(a,b), and a
b=a+b for a,b
R and extend this pair of operations to matrices and vectors in the same way as in conventional linear algebra, that is, if A=(aij),B=(bij),C=(cij) are real matrices or vectors of compatible sizes then C=AB if for all i,j. The symbol diag(d1,d2,…,dn) denotes the matrix D with diagonal elements equal to d1,d2,…,dn and off-diagonal elements equal to -∞. For an arbitrary parameter ε
R and given square matrices A=(aij), , we study the ℓ-parametric eigenproblem, i.e. problem of finding all xε=(x1(ε),x2(ε),…,xn(ε)) and λεℓ, satisfying
D. We introduce some properties of general ℓ-parametric eigenproblem and the O(n3) algorithm which gives all solutions of the 1-parametric eigenproblem with respect to ε. Keywords: Parametric eigenproblem; Max-algebra
MSC: primary: 90C27; secondary: 05B35
Article Outline
- 1. Introduction
- 2. Definitions and preliminary results
- 3. ℓ-Parametric eigenvalues
- 4. ℓ-Parametric eigenvectors
- 5. Computational aspects
- Acknowledgements
- Appendix
- References
