New iterative criteria for strong H $\mathcal{H}$ -tensors and an application

Abstract Strong H $\mathcal{H}$ -tensors play an important role in identifying the positive definiteness of even-order real symmetric tensors. In this paper, some new iterative criteria for identifying strong H $\mathcal{H}$ -tensors are obtained. These criteria only depend on the elements of the tensors, and it can be more effective to determine whether a given tensor is a strong H $\mathcal{H}$ -tensor or not by increasing the number of iterations. Some numerical results show the feasibility and effectiveness of the algorithm