H-tensor is a new developed concept which plays an important role in tensor analysis and computing. In this paper, we explore the properties of H-tensors and establish some new criteria for strong H-tensors. In partic...H-tensor is a new developed concept which plays an important role in tensor analysis and computing. In this paper, we explore the properties of H-tensors and establish some new criteria for strong H-tensors. In particular, based on the principal subtensor, we provide a new necessary and sufficient condition of strong H-tensors, and based on a type of generalized diagonal product dominance, we establish some new criteria for identifying strong H-tensors. The results obtained in this paper extend the corresponding conclusions for strong H-matrices and improve the existing results for strong H-tensors.展开更多
We study the relations between several classes of matrices with variants of the diagonal dominance property, and identify those classes which form pairs of incomparable classes. For an incomparable pair (X1,X2) of cla...We study the relations between several classes of matrices with variants of the diagonal dominance property, and identify those classes which form pairs of incomparable classes. For an incomparable pair (X1,X2) of classes of matrices with variants of the diagonal dominance property, we also study the problem of providing sufficient conditions for the matrices in Xi to be in Xj with {i,j}={1,2}. The article is a continuation of a series of articles on the topic and related topics by the author;see [1][2][3][4].展开更多
基金Acknowledgements The authors would like to give their sincere thanks to the anonymous referees for their valuable suggestions and helpful comments, which help improve the presen- tation of the paper. This work was supported by the National Natural Science Foundation of China （Grant No. 61572283）.
文摘H-tensor is a new developed concept which plays an important role in tensor analysis and computing. In this paper, we explore the properties of H-tensors and establish some new criteria for strong H-tensors. In particular, based on the principal subtensor, we provide a new necessary and sufficient condition of strong H-tensors, and based on a type of generalized diagonal product dominance, we establish some new criteria for identifying strong H-tensors. The results obtained in this paper extend the corresponding conclusions for strong H-matrices and improve the existing results for strong H-tensors.
文摘We study the relations between several classes of matrices with variants of the diagonal dominance property, and identify those classes which form pairs of incomparable classes. For an incomparable pair (X1,X2) of classes of matrices with variants of the diagonal dominance property, we also study the problem of providing sufficient conditions for the matrices in Xi to be in Xj with {i,j}={1,2}. The article is a continuation of a series of articles on the topic and related topics by the author;see [1][2][3][4].
