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M -Eigenvalues-Based Sufficient Conditions for the Positive Definiteness of Fourth-Order Partially Symmetric Tensors

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  • Gang Wang
  • Linxuan Sun
  • Lixia Liu

Abstract

M -eigenvalues of fourth-order partially symmetric tensors play important roles in the nonlinear elastic material analysis and the entanglement problem of quantum physics. In this paper, we introduce M -identity tensor and establish two M -eigenvalue inclusion intervals with n parameters for fourth-order partially symmetric tensors, which are sharper than some existing results. Numerical examples are proposed to verify the efficiency of the obtained results. As applications, we provide some checkable sufficient conditions for the positive definiteness and establish bound estimations for the M -spectral radius of fourth-order partially symmetric nonnegative tensors.

Suggested Citation

  • Gang Wang & Linxuan Sun & Lixia Liu, 2020. "M -Eigenvalues-Based Sufficient Conditions for the Positive Definiteness of Fourth-Order Partially Symmetric Tensors," Complexity, Hindawi, vol. 2020, pages 1-8, January.
    • Handle: RePEc:hin:complx:2474278
    DOI: 10.1155/2020/2474278
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    Cited by:

    1. Zhuolin Du & Chunyan Wang & Haibin Chen & Hong Yan, 2024. "An Efficient GIPM Algorithm for Computing the Smallest V-Singular Value of the Partially Symmetric Tensor," Journal of Optimization Theory and Applications, Springer, vol. 201(3), pages 1151-1167, June.
    2. Ying Zhang & Linxuan Sun & Gang Wang, 2020. "Sharp Bounds on the Minimum M -Eigenvalue of Elasticity M -Tensors," Mathematics, MDPI, vol. 8(2), pages 1-13, February.
    3. Zhao, Jianxing, 2023. "Conditions of strong ellipticity and calculations of M-eigenvalues for a partially symmetric tensor," Applied Mathematics and Computation, Elsevier, vol. 458(C).

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