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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, we analyse the Perron vector of an irreducible nonnegative tensor, and present some lower and upper bounds for the ratio of the smallest and largest entries of a Perron vector based on some new techniques, which always improve the existing ones. Applying these new ratio results, we first refine two-sided bounds for the spectral radius of an irreducible nonnegative tensor. In particular, for the matrix case, the new bounds also improve the corresponding ones. Second, we provide a new Ky Fan type theorem, which improves the existing one. Third, we refine the perturbation bound for the spectral radii of nonnegative tensors, from which one may derive a comparison theorem for spectral radii of nonnegative tensors. Numerical examples are given to show the efficiency of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study the global uniqueness and solvability (GUS-property) of tensor complementarity problems (TCPs) for some special structured tensors. The modulus equation for TCPs is also proposed, and based on this equation, we develop the corresponding nonsmooth Newton’s method, which extends the existing method given in the work of Zheng H and Li W. The modulus-based nonsmooth Newton’s method for solving linear complementarity problems. J Comput Appl Math. 2015;288: 116-126. Numerical examples are given to demonstrate the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Summary: The finite‐difference method applied to the time‐fractional subdiffusion equation usually leads to a large‐scale linear system with a block lower triangular Toeplitz coefficient matrix. The approximate inversion method is employed to solve this system. A sufficient condition is proved to guarantee the high accuracy of the approximate inversion method for solving the block lower triangular Toeplitz systems, which are easy to verify in practice and have a wide range of applications. The applications of this sufficient condition to several existing finite‐difference schemes are investigated. Numerical experiments are presented to verify the validity of theoretical results. [ABSTRACT FROM AUTHOR]