Nonsingular $H$-tensor and its criteria

By Yiju Wang, Guanglu Zhou, L. Caccetta. 2016

49 citations recorded by the source corpus.

$H$-tensor is a new developed concept in tensor analysis and it is an extension of $H$-matrix and $M$-tensor. Based on the spectral theory of nonnegative tensors, several equivalent conditions of nonsingular $H$-tensors are established in the literature. However, these conditions can not be used as a criteria to identify nonsingular $H$-tensors as they are hard to verify. In this paper, based on the diagonal product dominance and $S$ diagonal product dominance of a tensor, we establish some new implementable criteria in identifying nonsingular $H$-tensors. The positive definiteness of nonsingular $H$-tensors with positive diagonal entries is also discussed in this paper. The obtained results extend the corresponding conclusions for nonsingular $H$-matrices and improve the existing results for nonsingular $H$-tensors.

Subfields: Computational Mathematics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/f02c0134ad42ed91ebb7d7c10c1b758466845cad