Some new criteria for H-tensors are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor are given. The advantages of the results obtained are illustrated by numerical examples.
<abstract><p>Positive definite polynomials are important in the field of optimization. $ \mathcal{H} $-tensors play an important role in identifying the positive definiteness of an even-order homogeneous multivariate form. In this paper, we propose some new criterion for identifying $ \mathcal{H} $-tensor. As applications, we give new conditions for identifying positive definiteness of the even-order homogeneous multivariate form. At last, some numerical examples are provided to illustrate the efficiency and validity of new methods.</p></abstract>
Some new inequalities for the minimum eigenvalue of M-matrices are obtained. These inequalities improve existing results, and the estimating formulas are easier to calculate since they only depend on the entries of matrices. Finally, some examples are also given to show that the bounds are better than some previous results.
MSC: 15A18; 15A42
In this paper, new error bounds for the linear complementarity problem are obtained when the involved matrix is a weakly chained diagonally dominant B-matrix. The proposed error bounds are better than some existing results. The advantages of the results obtained are illustrated by numerical examples.
A new upper bound for the infinity norm of inverse matrix of a strictly diagonally dominant M-matrix is given, and the lower bound for the minimum eigenvalue of the matrix is obtained. Furthermore, an upper bound for the infinity norm of inverse matrix of a strictly α-diagonally dominant M-matrix is presented. Finally, we give numerical examples to illustrate our results. MSC: 15A42; 15A45
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