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
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.
In this paper,we consider the tensor absolute value equations(TAVEs),which is a newly introduced problem in the context of multilinear systems.Although the system of the TAVEs is an interesting generalization of matri...In this paper,we consider the tensor absolute value equations(TAVEs),which is a newly introduced problem in the context of multilinear systems.Although the system of the TAVEs is an interesting generalization of matrix absolute value equations(AVEs),the well-developed theory and algorithms for the AVEs are not directly applicable to the TAVEs due to the nonlinearity(or multilinearity)of the problem under consideration.Therefore,we first study the solutions existence of some classes of the TAVEs with the help of degree theory,in addition to showing,by fixed point theory,that the system of the TAVEs has at least one solution under some checkable conditions.Then,we give a bound of solutions of the TAVEs for some special cases.To find a solution to the TAVEs,we employ the generalized Newton method and report some preliminary results.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.
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Supported by the National Natural Science Foundation of China(11361074)the Foundation of Science and Technology Department of Guizhou Province([2015]7206)+1 种基金the Natural Science Programs of Education Department of Guizhou Province([2015]420)the Research Foundation of Guizhou Minzu University(15XRY004)
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.
基金Supported by the National Natural Science Foundation of China(11601473)the Foundation of Science and Technology Department of Guizhou Province(20191161,20181079)the Natural Science Programs of Education Department of Guizhou Province(2015420)
基金supported by National Natural Science Foundation of China(Grant Nos.11571087 and 11771113)Natural Science Foundation of Zhejiang Province(Grant No.LY17A010028)supported by the Hong Kong Research Grant Council(Grant Nos.PolyU 15302114,15300715,15301716 and 15300717)。
文摘In this paper,we consider the tensor absolute value equations(TAVEs),which is a newly introduced problem in the context of multilinear systems.Although the system of the TAVEs is an interesting generalization of matrix absolute value equations(AVEs),the well-developed theory and algorithms for the AVEs are not directly applicable to the TAVEs due to the nonlinearity(or multilinearity)of the problem under consideration.Therefore,we first study the solutions existence of some classes of the TAVEs with the help of degree theory,in addition to showing,by fixed point theory,that the system of the TAVEs has at least one solution under some checkable conditions.Then,we give a bound of solutions of the TAVEs for some special cases.To find a solution to the TAVEs,we employ the generalized Newton method and report some preliminary results.
