Criterions for identifying ℋ-tensors

Some Criteria for $${\varvec{\mathcal {H}}}$$-Tensors

“…In this paper, we establish some new criteria in identifying nonsingular H-tensors and give two numerical examples. These criteria are different from those of [1,6,7,9,10,12].…”

“…In [6,7], the authors provided an iterative algorithm for strong H-tensors, respectively. In [1,9,10,12], the authors gave some criteria for H-tensors. In [8], the authors gave some properties and conditions for H-tensors and nonsingular H-tensors.…”

“…The H-tensor which contains the M-tensor as special cases plays an important role in identifying positive definiteness of even-order real symmetric tensors [2,3,5,11]. In [1,6,7,9,10,12], the authors presented some criteria for H-tensors. In [8], the authors gave some properties and conditions for H-tensors and nonsingular H-tensors.…”

A new characterization of symmetric $H^+$-tensors and $M$-tensors

“…On the other hand, symmetric H + -tensors can be characterized using the notion of diagonally dominant tensors (see Definition 1). Most of the work related to H + -tensors makes use of the diagonal dominance property [see, e.g., 17,25,27,46,51]. We will also make use of this property in this work.…”

“…, 48]. In particular, we show (see Corollary 15 and (27)) that membership to the set of symmetric H + -tensors can be decided in polynomial time by solving a power cone optimization problem [see, e.g., 9,15] A lot of effort has been made to characterize H + -tensors [see, e.g., 17,25,27,29,46,49,51]. However, these articles typically focus on studying sufficient conditions for a tensor to be an H-tensor.…”