New iterative criteria for strong [Formula: see text]-tensors and an application

Strong [Formula: see text]-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 [Formula: see text]-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 [Formula: see text]-tensor or not by increasing the number of iterations. Some numerical results show the feasibility and effectiveness of the algorithm.