首页|Perron-Frobenius theory for some classes of nonnegative tensors in the max algebra
Perron-Frobenius theory for some classes of nonnegative tensors in the max algebra
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NSTL
Elsevier
An analog of Perron-Frobenius theory is proposed for some classes of nonnegative tensors in the max algebra. In the first part some important characterizations of nonnegative matrices can be extended to nonnegative tensors over max algebra, especially the Perron-Frobenius theorem for weakly irreducible nonnegative tensors and the Collatz-Wielandt minimax theorem for nonnegative tensors. Then, in the second part, an iterative method is proposed for finding the largest max eigenvalue of a nonnegative tensor based on diagonal similar tensors. The iterative method is convergent for weakly irreducible nonnegative tensors. Some numerical results are provided to illustrate the efficiency of the iterative method. (C) 2022 Elsevier Inc. All rights reserved.
Max algebraPerron-Frobenius theoryWeakly irreducible tensorsIterative methodGENERALIZED SPECTRAL-RADIUSLARGEST EIGENVALUEVERSIONCONVERGENCEALGORITHM
NSTL
Elsevier
