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arXiv · 1504.04668

Calculating max-eigenvalues and max-eigenvectors with jumps of matrices

Ali Ebadian·Saeed Hashemi Sababe·Hojr Shokouh Saljoughi
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Abstract

The eigenvalue problem for an irreducible non negative matrix $A=[a_{ij}]$ in the max-algebra is the form $A \otimes x = \lambda x$ where $(A \otimes x)_i = \max (a_{ij}x_j), x=(x_1,x_2, \dots, x_n)^t $ and $\lambda $ refers to maximum cycle geometric mean $\mu (A) $. In this paper we exhibit a method to compute $\mu (A)$ and max-eigenvector by using mutation of matrices. Since the order of power method algorithm is $O(n^3)$, the advantage of this paper present a faster procedure.

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Ali Ebadian, Saeed Hashemi Sababe, Hojr Shokouh Saljoughi. 2015-04-18. Calculating max-eigenvalues and max-eigenvectors with jumps of matrices. https://arxiv.org/abs/1504.04668

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