M-Eigenvalues-Based Sufficient Conditions for the Positive Definiteness of Fourth-Order Partially Symmetric Tensors
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-ord...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/2474278 |
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| _version_ | 1832553741948026880 |
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| author | Gang Wang Linxuan Sun Lixia Liu |
| author_facet | Gang Wang Linxuan Sun Lixia Liu |
| author_sort | Gang Wang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4fad86335a2a4e9ab1af615acebc5ea2 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-4fad86335a2a4e9ab1af615acebc5ea22025-02-03T05:53:21ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/24742782474278M-Eigenvalues-Based Sufficient Conditions for the Positive Definiteness of Fourth-Order Partially Symmetric TensorsGang Wang0Linxuan Sun1Lixia Liu2School of Management Science, Qufu Normal University, Rizhao, Shandong 276800, ChinaSchool of Management Science, Qufu Normal University, Rizhao, Shandong 276800, ChinaSchool of Mathematics and Statistics, Xidian University, Xi’an, Shanxi 710071, ChinaM-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.http://dx.doi.org/10.1155/2020/2474278 |
| spellingShingle | Gang Wang Linxuan Sun Lixia Liu M-Eigenvalues-Based Sufficient Conditions for the Positive Definiteness of Fourth-Order Partially Symmetric Tensors Complexity |
| title | M-Eigenvalues-Based Sufficient Conditions for the Positive Definiteness of Fourth-Order Partially Symmetric Tensors |
| title_full | M-Eigenvalues-Based Sufficient Conditions for the Positive Definiteness of Fourth-Order Partially Symmetric Tensors |
| title_fullStr | M-Eigenvalues-Based Sufficient Conditions for the Positive Definiteness of Fourth-Order Partially Symmetric Tensors |
| title_full_unstemmed | M-Eigenvalues-Based Sufficient Conditions for the Positive Definiteness of Fourth-Order Partially Symmetric Tensors |
| title_short | M-Eigenvalues-Based Sufficient Conditions for the Positive Definiteness of Fourth-Order Partially Symmetric Tensors |
| title_sort | m eigenvalues based sufficient conditions for the positive definiteness of fourth order partially symmetric tensors |
| url | http://dx.doi.org/10.1155/2020/2474278 |
| work_keys_str_mv | AT gangwang meigenvaluesbasedsufficientconditionsforthepositivedefinitenessoffourthorderpartiallysymmetrictensors AT linxuansun meigenvaluesbasedsufficientconditionsforthepositivedefinitenessoffourthorderpartiallysymmetrictensors AT lixialiu meigenvaluesbasedsufficientconditionsforthepositivedefinitenessoffourthorderpartiallysymmetrictensors |