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In this paper, we propose several improved uniqueness conditions of solution for multilinear PageRank with order-3 irreducible stochastic tensors. By considering upper and lower bounds of solutions, the refined uniqueness conditions are more effective than the existing ones. Furthermore, as an application, sharp perturbation bounds for multilinear PageRank are also developed basing on the new uniqueness conditions. Numerical examples are given to verify the efficiency of the proposed uniqueness conditions. [ABSTRACT FROM AUTHOR]

In this paper, firstly, we introduce the variant tensor splittings, and present some equivalent conditions for a strong M -tensor based on the tensor splitting. Secondly, the existence and uniqueness conditions of the solution for multi-linear systems are given. Thirdly, we propose some tensor splitting algorithms for solving multi-linear systems with coefficient tensor being a strong M -tensor. As an application, a tensor splitting algorithm for solving the multi-linear model of higher order Markov chains is proposed. Numerical examples are given to demonstrate the efficiency of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Z -eigenpair of a tensor, in particular, an irreducible nonnegative tensor. We present some bounds for the eigenvector and Z -spectral radius. The proposed bounds improve some existing ones. An example with practical applications is given to show the proposed bound. [ABSTRACT FROM AUTHOR]