scholarly journals Bounds for the M-spectral radius of a fourth-order partially symmetric tensor

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Suhua Li ◽  
Yaotang Li
Keyword(s):  
Spectral Radius ◽  
Fourth Order ◽  
Symmetric Tensor ◽  
Partially Symmetric

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

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Gang Wang ◽  
Linxuan Sun ◽  
Lixia Liu
Keyword(s):  
Spectral Radius ◽  
Fourth Order ◽  
Quantum Physics ◽  
Sufficient Conditions ◽  
Positive Definiteness ◽  
Symmetric Tensors ◽  
Nonlinear Elastic Material ◽  
Numerical Examples ◽  
Nonlinear Elastic ◽  
Partially Symmetric

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.

l k,s -Singular values and spectral radius of partially symmetric rectangular tensors

2015 ◽  
Vol 11 (3) ◽  
pp. 605-622 ◽  
Author(s):  
Hongmei Yao ◽  
Bingsong Long ◽  
Changjiang Bu ◽  
Jiang Zhou
Keyword(s):  
Spectral Radius ◽  
Singular Values ◽  
Rectangular Tensors ◽  
Partially Symmetric

scholarly journals Sharp upper bounds on the maximum $M$-eigenvalue of fourth-order partially symmetric nonnegative tensors

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yuyan Yao ◽  
Gang Wang
Keyword(s):  
Fourth Order ◽  
Elastic Material ◽  
Quantum Physics ◽  
Upper Bounds ◽  
Nonlinear Elastic Material ◽  
Numerical Examples ◽  
Nonnegative Tensors ◽  
Material Analysis ◽  
Nonlinear Elastic ◽  
Partially Symmetric

<p style='text-indent:20px;'><inline-formula><tex-math id="M1">\begin{document}$ M $\end{document}</tex-math></inline-formula>-eigenvalues of partially symmetric nonnegative tensors play important roles in the nonlinear elastic material analysis and the entanglement problem of quantum physics. In this paper, we establish two upper bounds for the maximum <inline-formula><tex-math id="M2">\begin{document}$ M $\end{document}</tex-math></inline-formula>-eigenvalue of partially symmetric nonnegative tensors, which improve some existing results. Numerical examples are proposed to verify the efficiency of the obtained results.</p>

scholarly journals On the M-eigenvalue estimation of fourth-order partially symmetric tensors

2020 ◽  
Vol 16 (1) ◽  
pp. 309-324 ◽  
Author(s):  
Haitao Che ◽  
◽  
Haibin Chen ◽  
Yiju Wang ◽  
Keyword(s):  
Fourth Order ◽  
Symmetric Tensors ◽  
Eigenvalue Estimation ◽  
Partially Symmetric

scholarly journals New Sufficient Condition for the Positive Definiteness of Fourth Order Tensors

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 303 ◽  
Author(s):  
Jun He ◽  
Yanmin Liu ◽  
Junkang Tian ◽  
Zhuanzhou Zhang
Keyword(s):  
Spectral Radius ◽  
Fourth Order ◽  
Upper Bound ◽  
Positive Definiteness ◽  
Sufficient Condition ◽  
Numerical Examples ◽  
Eigenvalue Localization ◽  
Weakly Symmetric ◽  
Localization Set

In this paper, we give a new Z-eigenvalue localization set for Z-eigenvalues of structured fourth order tensors. As applications, a sharper upper bound for the Z-spectral radius of weakly symmetric nonnegative fourth order tensors is obtained and a new Z-eigenvalue based sufficient condition for the positive definiteness of fourth order tensors is also presented. Finally, numerical examples are given to verify the efficiency of our results.

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