The H-tensor is a new developed concept in tensor analysis and it is an extension of the M-tensor.In this paper,we present some criteria for identifying nonsingular H-tensors and give two numerical examples.
StrongH-tensors play a significant role in identifying the positive definiteness of an even-order real symmetric tensor.In this paper,first,an improved iterative algorithm is proposed to determine whether a given tens...StrongH-tensors play a significant role in identifying the positive definiteness of an even-order real symmetric tensor.In this paper,first,an improved iterative algorithm is proposed to determine whether a given tensor is a strong H-tensor,and the validity of the iterative algorithm is proved theoretically.Second,the iterative algorithm is employed to identify the positive definiteness of an even-order real symmetric tensor.Finally,numerical examples are presented to illustrate the advantages of the proposed algorithm.展开更多
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
The H-matrices are an important class in the matrix theory, and have many applications. Recently, this concept has been extended to higher order H-tensors. In this paper, we establish important properties of diagonall...The H-matrices are an important class in the matrix theory, and have many applications. Recently, this concept has been extended to higher order H-tensors. In this paper, we establish important properties of diagonally dominant tensors and H-tensors. Distributions of eigenvalues of nonsingular symmetricH-tensors are given. An J（t%-tensor is semi-positive, which enlarges the area of semi-positive tensor from H-tensor to H＋-tensor. The spectral radius of Jacobi tensor of a nonsingular （resp. singular） H-tensor is less than （resp. equal to） one. In particular, we show that a quasi-diagonally dominant tensor is a nonsingular H-tensor if and only if all of its principal sub-tensors are nonsingular H-tensors. An irreducible tensor H is an H-tensor if and only if it is quasi-diagonally dominant.展开更多
Some new criteria for identifying H-tensors are obtained. As applications, some sufficient conditions of the positive definiteness for an even- order real symmetric tensor are given, as well as a new eigenvalue inclus...Some new criteria for identifying H-tensors are obtained. As applications, some sufficient conditions of the positive definiteness for an even- order real symmetric tensor are given, as well as a new eigenvalue inclusion region for tensors is established. It is proved that the new eigenvalue inclusion region is tighter than that of Y. Yang and Q. Yang [SIAM J. Matrix Anal. Appl., 2010, 31： 2517-2530]. Numerical examples are reported to demonstrate the corresponding results.展开更多
H-tensor plays an important role in identifying positive definiteness of even order real symmetric tensors.In this paper,some definitions and theorems related to H-tensors are introducedfirstly.Secondly,some new criteria...H-tensor plays an important role in identifying positive definiteness of even order real symmetric tensors.In this paper,some definitions and theorems related to H-tensors are introducedfirstly.Secondly,some new criteria for identifying nonsingular H-tensors are proposed,moreover,a new theorem for identifying positive definiteness of even order real symmetric tensors is obtained.Finally,some numerical examples are given to illustrate our results.展开更多
基金This work was supported by the National Nature Science Foundation of China(Grants no.11771275)the Science and Technology Program of Shandong Universities(no.J16LI04).
文摘The H-tensor is a new developed concept in tensor analysis and it is an extension of the M-tensor.In this paper,we present some criteria for identifying nonsingular H-tensors and give two numerical examples.
文摘StrongH-tensors play a significant role in identifying the positive definiteness of an even-order real symmetric tensor.In this paper,first,an improved iterative algorithm is proposed to determine whether a given tensor is a strong H-tensor,and the validity of the iterative algorithm is proved theoretically.Second,the iterative algorithm is employed to identify the positive definiteness of an even-order real symmetric tensor.Finally,numerical examples are presented to illustrate the advantages of the proposed algorithm.
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.
基金Acknowledgements The authors would like to thank Professors Liqun Qi and Yiju Wang for their comments and the preprint [14]. They would like to thank two referees for their detailed suggestions which greatly improve the presentation. They also thank Prof. Liqun Qi for kindly reminding them of the very recent paper [12] after their first revision in February, 2015. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11171371, 11271084.）
文摘The H-matrices are an important class in the matrix theory, and have many applications. Recently, this concept has been extended to higher order H-tensors. In this paper, we establish important properties of diagonally dominant tensors and H-tensors. Distributions of eigenvalues of nonsingular symmetricH-tensors are given. An J（t%-tensor is semi-positive, which enlarges the area of semi-positive tensor from H-tensor to H＋-tensor. The spectral radius of Jacobi tensor of a nonsingular （resp. singular） H-tensor is less than （resp. equal to） one. In particular, we show that a quasi-diagonally dominant tensor is a nonsingular H-tensor if and only if all of its principal sub-tensors are nonsingular H-tensors. An irreducible tensor H is an H-tensor if and only if it is quasi-diagonally dominant.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant Nos. 11361074, 11326242） and the Science Foundation of the Education Department of Yunnan Province （Grant No. 2013FD002）.
文摘Some new criteria for identifying H-tensors are obtained. As applications, some sufficient conditions of the positive definiteness for an even- order real symmetric tensor are given, as well as a new eigenvalue inclusion region for tensors is established. It is proved that the new eigenvalue inclusion region is tighter than that of Y. Yang and Q. Yang [SIAM J. Matrix Anal. Appl., 2010, 31： 2517-2530]. Numerical examples are reported to demonstrate the corresponding results.
基金supported by the National Natural Science Foundations of China(Grant No.31600299)The Natural Science Foundation of Shaanxi province(Grant No.2020JM-622).
文摘H-tensor plays an important role in identifying positive definiteness of even order real symmetric tensors.In this paper,some definitions and theorems related to H-tensors are introducedfirstly.Secondly,some new criteria for identifying nonsingular H-tensors are proposed,moreover,a new theorem for identifying positive definiteness of even order real symmetric tensors is obtained.Finally,some numerical examples are given to illustrate our results.
