Abstract
M-eigenvalues of a fourth-order partially symmetric tensor play an important role in the nonlinear elastic material analysis and the entanglement problem in quantum physics. But it is not easy to get the M-eigenvalues exactly, especially for high dimensional fourth-order partially symmetric tensors. In this paper, we give two M-eigenvalue inclusion intervals for a fourth-order partially symmetric tensor, which provide two upper bounds for the M-spectral radius. As an application, taking these upper bounds as the parameter τ in WQZ-algorithm presented by Wang et al. (2009), respectively, can make the generated sequence by this algorithm more rapidly converge to a good approximation of the largest M-eigenvalue of a fourth-order partially symmetric tensor.
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