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A class of weakly irreducible quasi-positive tensors is defined by using directed hypergraphs of tensors, which generalizes the essential positive tensors, weakly positive tensors, generalized weakly positive tensors, and weakly essential irreducible nonnegative tensors. Furthermore, an algorithm based on displacement transformation for computing theHH-spectral radius of such weakly irreducible quasi-positive tensors is discussed. TheRR-linear convergence of the proposed algorithm is established, and the conditions are also provided to ensure its linear convergence.

Algorithm and linear convergence of the H -spectral radius of weakly irreducible quasi-positive tensors