Programmable criteria for strong $\mathcal {H}$-tensors

Strong \(\mathcal {H}\)-tensors play an important role in identifying positive semidefiniteness of even-order real symmetric tensors. We provide several simple practical criteria for identifying strong \(\mathcal {H}\)-tensors. These criteria only depend on the elements of the tensors; therefore, they are easy to be verified. Meanwhile, a sufficient and necessary condition of strong \(\mathcal {H}\)-tensors is obtained. We also propose an algorithm for identifying the strong \(\mathcal {H}\)-tensors based on these criterions. Some numerical results show the feasibility and effectiveness of the algorithm.