On the Power Method in Max Algebra
نویسنده
چکیده
The eigenvalue problem for an irreducible nonnegative matrix A = a ij ] in the max algebra system is A x = x, where (A x) i = max j (a ij x j) and turns out to be the maximum circuit geometric mean, (A). A power method algorithm is given to compute (A) and eigenvector x. This method generalizes and simpliies an algorithm due to Braker and Olsder. The algorithm is developed by using results on the convergence of max powers of A. These results are proved using nonnegative matrix theory. Some asymptotic formulas relating (A), the spectral radius and norms are also given.
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