Jianxing Zhao

New practical criteria for ℋ-tensors and its application

Several new criteria for identifying -tensors are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor are given. Advantages of the obtained results are illustrated by numerical examples.

A new Z -eigenvalue localization set for tensors

A new Z-eigenvalue localization set for tensors is given and proved to be tighter than those in the work of Wang et al. (Discrete Contin. Dyn. Syst., Ser. B 22(1):187-198, 2017). Based on this set, a sharper upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors is obtained. Finally, numerical examples are given to verify the theoretical results.

Singular value inclusion sets for rectangular tensors

Abstract Two singular value inclusion sets for rectangular tensors are given. These sets provide two upper bounds and lower bounds for the largest singular value of nonnegative rectangular tensors, which can be taken as a parameter of an algorithm presented by Zhou et al. (Linear Algebra Appl. 2013; 438: 959–968) such that the sequences produced by this algorithm converge rapidly to the largest singular value of an irreducible nonnegative rectangular tensor.

Two new singular value inclusion sets for rectangular tensors

ABSTRACT Let be a real th order dimensional rectangular tensor. A new singular value inclusion set for rectangular tensors with m=n is given and proved to be tighter than those in [Zhao JX, Li CQ. Singular value inclusion sets for rectangular tensors. Linear Multilinear A. 2018;66(7):1333–1350] and [Sang CL. An S-type singular value inclusion set for rectangular tensors. J Inequal Appl. 2017;2017:141]. Soon afterwards, this new singular value inclusion set is generalized to the general case, that is, m and n are not necessarily equal. As an application of the two sets, two upper bounds and lower bounds for the largest singular value of nonnegative rectangular tensors are obtained.

SGB-tensors and its applications

ABSTRACT In this paper, we propose two new classes of tensors: SGB-tensors and -tensors, which provide checkable sufficient conditions for the positive (semi-)definiteness of tensors, and get an interval which contains all H-eigenvalues of a given even order real symmetric tensor by applying SGB-tensors.

The disc separation and the eigenvalue distribution of the Schur complement of nonstrictly diagonally dominant matrices

The result on the Geršgorin disc separation from the origin for strictly diagonally dominant matrices and their Schur complements in (Liu and Zhang in SIAM J. Matrix Anal. Appl. 27(3):665-674, 2005) is extended to nonstrictly diagonally dominant matrices and their Schur complements, showing that under some conditions the separation of the Schur complement of a nonstrictly diagonally dominant matrix is greater than that of the original grand matrix. As an application, the eigenvalue distribution of the Schur complement is discussed for nonstrictly diagonally dominant matrices to derive some significant conclusions. Finally, some examples are provided to show the effectiveness of theoretical results.

A new S-type upper bound for the largest singular value of nonnegative rectangular tensors

By breaking N={1,2,…,n}

A new eigenvalue inclusion set for tensors with its applications

N=\{1,2,\ldots,n\}

Two new lower bounds for the minimum eigenvalue of M -tensors

into disjoint subsets S and its complement, a new S-type upper bound for the largest singular value of nonnegative rectangular tensors is given and proved to be better than some existing ones. Numerical examples are given to verify the theoretical results.

Several new inequalities for the minimum eigenvalue of M-matrices

In this paper, we give a new eigenvalue localization set for tensors and show that the new set is tighter than those presented by Qi (2005) and Li et al. (2014). As applications, we give a new sufficient condition of the positive (semi-)definiteness for an even-order real symmetric tensor and new lower and upper bounds of the minimum eigenvalue for -tensors.