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

2015/04/18 by Ebadian, Ali, Sababe, Saeed Hashemi, Saljoughi, Hojr Shokouh
#15A18 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1504.04668

Abstract

The eigenvalue problem for an irreducible non negative matrix A=[a_ij] in the max-algebra is the form A ⊗ x = λx where (A ⊗ x)_i = max (a_ijx_j), x=(x₁,x₂, …, x_n)^t and λ refers to maximum cycle geometric mean μ(A) . In this paper we exhibit a method to compute μ(A) and max-eigenvector by using mutation of matrices. Since the order of power method algorithm is O(n³), the advantage of this paper present a faster procedure.

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