Parameterized S-type M-eigenvalue inclusion intervals for fourth-order partially symmetric tensors and its applications

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Abstract
In this article, based on M-identity tensor, we establish some parameterized S-type inclusion intervals for fourth-order partially symmetric tensors. The new inclusion intervals are tighter than some existing results. Furthermore, some new S-type upper bounds on the M-spectral radius of fourth-order partially symmetric tensors are obtained. As applications, the new S-type upper bounds as the parameter of WQZ-algorithm can make the algorithm more rapidly converge to the largest M-eigenvalue of fourth-order partially symmetric tensors. Finally, we propose two sufficient conditions for the M-positive definiteness of fourth-order partially symmetric tensors.