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Eigenproblem for monotone and Toeplitz matrices in a max-algebra. (English) Zbl 1079.93033
Summary: The eigenproblem for monotone and Toeplitz matrices in a max-algebra is shown to be solvable in $$O(n^2)$$ time. Two algorithms are described which, for a given $$n \times n$$ real monotone and for a given $$n\times n$$ real Toeplitz matrix compute an eigenvalue $${\lambda}$$; and all eigenvectors of the form $$x = (x_1, x_2, \dots , x_n)$$ such that
$\max (a_{ij} + x_j) = \lambda + x_i \text{ for \;all } i = 1,2,\dots,n.$
These results improve standard $$O(n^3)$$ algorithms used in the general case.

##### MSC:
 93C65 Discrete event control/observation systems 05B35 Combinatorial aspects of matroids and geometric lattices 90C27 Combinatorial optimization
##### Keywords:
monotone matrix; Toeplitz matrix
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##### References:
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