Criteria For Nonsingular H-matrices And The Estimation Of The Spectral Radius Of The Tensor

Nonsingular H-matrix is a kind of special but very important matrix, it plays a non-ignorable role in many areas, such as matrix theory and quantitative economics, probability and statistics, control theory, theory of power system, neural network and mathematical physics, social science and so on. However, how to determine whether a given matrix is nonsingular H-matrices is a basic but difficult problem. Recently, many scholars at home and abroad have studied in this area and given the nonsingular H-matrices some effective discriminant method. In this thesis, we will give a more wide and effective criteria for nonsingular H-matrix on the basis of diagonal matrix factors by using the knowledge of nonzero elements chain matrix and irreducible matrix, and the technique of reduction of inequality, and improves some existing results, and at the same time we give some examples to illustrate the validity and practicability of the results.On the other hand, tensor as a higher-order generalization of matrix, it still retains many properties of matrix. And tensor has been widely used in such as blind source separation, magnetic resonance imaging, nonlinear optimization and high order statistics, and so on. Therefore, in this paper we will also study tensor, we mainly consider the estimate of the spectral radius of tensor, by study the eigenvalue problem about tensor, we give a bound for the spectral radius of nonnegative tensors and prove that the new bound is better than those in the literature. The concrete examples also illustrate the validity and practicability of the obtained results.