Abstract
In this paper, we focus on Perron pairs of a nonnegative tensor, which have wide applications in many areas, such as higher order Markov chains and hypergraph theory. We first propose a SemiDefinite Programming (SDP) relaxation algorithm to directly compute all Perron eigenvectors of a nonnegative tensor with finite Perron eigenvectors, where all Perron eigenvectors associated with monotonous Perron eigenvalues are generated by solving finite SDP problems. Then, the convergence of the proposed algorithm is proved. Finally, numerical experiments illustrate the efficiency of the proposed algorithm.
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