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

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Jingjing Cui, Guohua Peng, Quan Lu, Zhengge Huang

Author Information

Jingjing Cui: Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072 P.R. China.
Guohua Peng: Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072 P.R. China.
Quan Lu: Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072 P.R. China.
Zhengge Huang: Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072 P.R. China.

PMID: 28298873 DOI: 10.1186/s13660-017-1323-1

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.

irreducible non-zero elements chain positive definiteness strong [Formula: see text]-tensors

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