Figure 1.
$C(\mathcal{A}_{0})\nsubseteqq V(\mathcal{A}_{0})$ and $C(\mathcal{A}_{0})\nsupseteqq V(\mathcal{A}_{0})$ .
-
Previous Article
Optimal threshold strategies with capital injections in a spectrally negative Lévy risk model
- JIMO Home
- This Issue
-
Next Article
Asymptotics for a bidimensional risk model with two geometric Lévy price processes
April
2019, 15(2): 507-516.
doi: 10.3934/jimo.2018054
Exclusion sets in the Δ-type eigenvalue inclusion set for tensors
School of Mathematics and Statistics, Yunnan University, Kunming 650091, China |
By excluding some sets which don't include any eigenvalue of a given tensor from the Δ-type eigenvalue inclusion set, two new Δ-type eigenvalue inclusion sets of tensors are given. And two criteria for identifying nonsingular tensors are also provided by using the new Δ-type eigenvalue inclusion sets.
Mathematics Subject Classification:
Primary: 15A18, 15A69.
Citation:
Yaotang Li, Suhua Li. Exclusion sets in the Δ-type eigenvalue inclusion set for tensors. Journal of Industrial and Management Optimization,
2019, 15
(2)
: 507-516.
doi: 10.3934/jimo.2018054
![]()
References:
| [1] |
C. Bu, Y. Wei, L. Sun and J. Zhou,
Brualdi-type eigenvalue inclusion sets of tensors, Linear Algebra and its Applications, 480 (2015), 168-175.
doi: 10.1016/j.laa.2015.04.034. |
| [2] |
C. J. Hillar and L. -H. Lim, Most tensor problems are NP-hard, Journal of the ACM (JACM), 60 (2013), Art. 45, 39 pp. |
| [3] |
S. Hu, Z. Huang, C. Ling and L. Qi,
On determinants and eigenvalue theory of tensors, Journal of Symbolic Computation, 50 (2013), 508-531.
doi: 10.1016/j.jsc.2012.10.001. |
| [4] |
Z. Huang, L. Wang, Z. Xu and J. Cui, A new S-type eigenvalue inclusion set for tensors and its applications, Journal of Inequalities and Applications, 2016 (2016), Paper No. 254, 19 pp. |
| [5] |
C. Li, Y. Li and X. Kong,
New eigenvalue inclusion sets for tensors, Numerical Linear Algebra with Applications, 21 (2014), 39-50.
doi: 10.1002/nla.1858. |
| [6] |
C. Li and Y. Li,
An eigenvalue localization set for tensors with applications to determine the positive (semi-) definiteness of tensors, Linear and Multilinear Algebra, 64 (2016), 587-601.
doi: 10.1080/03081087.2015.1049582. |
| [7] |
C. Li, Z. Chen and Y. Li,
A new eigenvalue inclusion set for tensors and its applications, Linear Algebra and its Applications, 481 (2015), 36-53.
doi: 10.1016/j.laa.2015.04.023. |
| [8] |
C. Li, A. Jiao and Y. Li,
An S-type eigenvalue localization set for tensors, Linear Algebra and its Applications, 493 (2016), 469-483.
doi: 10.1016/j.laa.2015.12.018. |
| [9] |
C. Li, J. Zhou and Y. Li,
A new Brauer-type eigenvalue localization set for tensors, Linear and Multilinear Algebra, 64 (2016), 727-736.
doi: 10.1080/03081087.2015.1119779. |
| [10] |
L. -H. Lim, Singular values and eigenvalues of tensors: A variational approach, in CAMSAP'05: Proceeding of the IEEE International Workshop on Computational Advances in MultiSensor Adaptive Processing, 2005,129–132. |
| [11] |
L. Qi,
Eigenvalues of a real supersymmetric tensor, Journal of Symbolic Computation, 40 (2005), 1302-1324.
doi: 10.1016/j.jsc.2005.05.007. |
| [12] |
L. Qi, Eigenvalues of a Supersymmetric Tensor and Positive Definiteness of an Even Degree Multivariate Form, Department of Applied Mathematics, The Hong Kong Polytechnic University, 2004. |
| [13] |
C. Sang and J. Zhao, A new eigenvalue inclusion set for tensors with its applications, Cogent Mathematics, 4 (2017), 1320831.
doi: 10.1080/23311835.2017.1320831. |
| [14] |
X. Wang and Y. Wei,
H-tensors and nonsingular H-tensors, Frontiers of Mathematics in China, 11 (2016), 557-575.
doi: 10.1007/s11464-015-0495-6. |
| [15] |
Y. Yang and Q. Yang,
Further results for Perron-Frobenius theorem for nonnegative tensors, SIAM Journal on Matrix Analysis and Applications, 31 (2010), 2517-2530.
doi: 10.1137/090778766. |
| [16] |
Q. Yang and Y. Yang,
Further results for Perron-Frobenius theorem for nonnegative tensors Ⅱ, SIAM Journal on Matrix Analysis and Applications, 32 (2011), 1236-1250.
doi: 10.1137/100813671. |
show all references
References:
| [1] |
C. Bu, Y. Wei, L. Sun and J. Zhou,
Brualdi-type eigenvalue inclusion sets of tensors, Linear Algebra and its Applications, 480 (2015), 168-175.
doi: 10.1016/j.laa.2015.04.034. |
| [2] |
C. J. Hillar and L. -H. Lim, Most tensor problems are NP-hard, Journal of the ACM (JACM), 60 (2013), Art. 45, 39 pp. |
| [3] |
S. Hu, Z. Huang, C. Ling and L. Qi,
On determinants and eigenvalue theory of tensors, Journal of Symbolic Computation, 50 (2013), 508-531.
doi: 10.1016/j.jsc.2012.10.001. |
| [4] |
Z. Huang, L. Wang, Z. Xu and J. Cui, A new S-type eigenvalue inclusion set for tensors and its applications, Journal of Inequalities and Applications, 2016 (2016), Paper No. 254, 19 pp. |
| [5] |
C. Li, Y. Li and X. Kong,
New eigenvalue inclusion sets for tensors, Numerical Linear Algebra with Applications, 21 (2014), 39-50.
doi: 10.1002/nla.1858. |
| [6] |
C. Li and Y. Li,
An eigenvalue localization set for tensors with applications to determine the positive (semi-) definiteness of tensors, Linear and Multilinear Algebra, 64 (2016), 587-601.
doi: 10.1080/03081087.2015.1049582. |
| [7] |
C. Li, Z. Chen and Y. Li,
A new eigenvalue inclusion set for tensors and its applications, Linear Algebra and its Applications, 481 (2015), 36-53.
doi: 10.1016/j.laa.2015.04.023. |
| [8] |
C. Li, A. Jiao and Y. Li,
An S-type eigenvalue localization set for tensors, Linear Algebra and its Applications, 493 (2016), 469-483.
doi: 10.1016/j.laa.2015.12.018. |
| [9] |
C. Li, J. Zhou and Y. Li,
A new Brauer-type eigenvalue localization set for tensors, Linear and Multilinear Algebra, 64 (2016), 727-736.
doi: 10.1080/03081087.2015.1119779. |
| [10] |
L. -H. Lim, Singular values and eigenvalues of tensors: A variational approach, in CAMSAP'05: Proceeding of the IEEE International Workshop on Computational Advances in MultiSensor Adaptive Processing, 2005,129–132. |
| [11] |
L. Qi,
Eigenvalues of a real supersymmetric tensor, Journal of Symbolic Computation, 40 (2005), 1302-1324.
doi: 10.1016/j.jsc.2005.05.007. |
| [12] |
L. Qi, Eigenvalues of a Supersymmetric Tensor and Positive Definiteness of an Even Degree Multivariate Form, Department of Applied Mathematics, The Hong Kong Polytechnic University, 2004. |
| [13] |
C. Sang and J. Zhao, A new eigenvalue inclusion set for tensors with its applications, Cogent Mathematics, 4 (2017), 1320831.
doi: 10.1080/23311835.2017.1320831. |
| [14] |
X. Wang and Y. Wei,
H-tensors and nonsingular H-tensors, Frontiers of Mathematics in China, 11 (2016), 557-575.
doi: 10.1007/s11464-015-0495-6. |
| [15] |
Y. Yang and Q. Yang,
Further results for Perron-Frobenius theorem for nonnegative tensors, SIAM Journal on Matrix Analysis and Applications, 31 (2010), 2517-2530.
doi: 10.1137/090778766. |
| [16] |
Q. Yang and Y. Yang,
Further results for Perron-Frobenius theorem for nonnegative tensors Ⅱ, SIAM Journal on Matrix Analysis and Applications, 32 (2011), 1236-1250.
doi: 10.1137/100813671. |
Figure 2.
$C(\mathcal{A}_{1})\subset \Theta(\mathcal{A}_{1})$ .
Figure 3.
$V(\mathcal{A}_{2})\subset \Theta(\mathcal{A}_{2})$ .
| [1] |
Yang Xu, Zheng-Hai Huang. Pareto eigenvalue inclusion intervals for tensors. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022035 |
| [2] |
Gang Wang, Guanglu Zhou, Louis Caccetta. Z-Eigenvalue Inclusion Theorems for Tensors. Discrete and Continuous Dynamical Systems - B, 2017, 22 (1) : 187-198. doi: 10.3934/dcdsb.2017009 |
| [3] |
Gang Wang, Yuan Zhang. $ Z $-eigenvalue exclusion theorems for tensors. Journal of Industrial and Management Optimization, 2020, 16 (4) : 1987-1998. doi: 10.3934/jimo.2019039 |
| [4] |
Kaiping Liu, Haitao Che, Haibin Chen, Meixia Li. Parameterized S-type M-eigenvalue inclusion intervals for fourth-order partially symmetric tensors and its applications. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022077 |
| [5] |
Chaoqian Li, Yajun Liu, Yaotang Li. Note on $ Z $-eigenvalue inclusion theorems for tensors. Journal of Industrial and Management Optimization, 2021, 17 (2) : 687-693. doi: 10.3934/jimo.2019129 |
| [6] |
Caili Sang, Zhen Chen. $ E $-eigenvalue localization sets for tensors. Journal of Industrial and Management Optimization, 2020, 16 (4) : 2045-2063. doi: 10.3934/jimo.2019042 |
| [7] |
Jun He, Guangjun Xu, Yanmin Liu. New Z-eigenvalue localization sets for tensors with applications. Journal of Industrial and Management Optimization, 2022, 18 (3) : 2095-2108. doi: 10.3934/jimo.2021058 |
| [8] |
Caili Sang, Zhen Chen. Optimal $ Z $-eigenvalue inclusion intervals of tensors and their applications. Journal of Industrial and Management Optimization, 2022, 18 (4) : 2435-2468. doi: 10.3934/jimo.2021075 |
| [9] |
Gang Wang, Yiju Wang, Yuan Zhang. Brualdi-type inequalities on the minimum eigenvalue for the Fan product of M-tensors. Journal of Industrial and Management Optimization, 2020, 16 (5) : 2551-2562. doi: 10.3934/jimo.2019069 |
| [10] |
Xifu Liu, Shuheng Yin, Hanyu Li. C-eigenvalue intervals for piezoelectric-type tensors via symmetric matrices. Journal of Industrial and Management Optimization, 2021, 17 (6) : 3349-3356. doi: 10.3934/jimo.2020122 |
| [11] |
Zhen Wang, Wei Wu. Bounds for the greatest eigenvalue of positive tensors. Journal of Industrial and Management Optimization, 2014, 10 (4) : 1031-1039. doi: 10.3934/jimo.2014.10.1031 |
| [12] |
Mohsen Tourang, Mostafa Zangiabadi, Chaoqian Li. Generalized minimal Gershgorin set for tensors. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022106 |
| [13] |
Yining Gu, Wei Wu. New bounds for eigenvalues of strictly diagonally dominant tensors. Numerical Algebra, Control and Optimization, 2018, 8 (2) : 203-210. doi: 10.3934/naco.2018012 |
| [14] |
Yannan Chen, Jingya Chang. A trust region algorithm for computing extreme eigenvalues of tensors. Numerical Algebra, Control and Optimization, 2020, 10 (4) : 475-485. doi: 10.3934/naco.2020046 |
| [15] |
Fei-Ying Yang, Wan-Tong Li, Jian-Wen Sun. Principal eigenvalues for some nonlocal eigenvalue problems and applications. Discrete and Continuous Dynamical Systems, 2016, 36 (7) : 4027-4049. doi: 10.3934/dcds.2016.36.4027 |
| [16] |
Mihai Mihăilescu. An eigenvalue problem possessing a continuous family of eigenvalues plus an isolated eigenvalue. Communications on Pure and Applied Analysis, 2011, 10 (2) : 701-708. doi: 10.3934/cpaa.2011.10.701 |
| [17] |
Abdessatar Khelifi, Siwar Saidani. Asymptotic behavior of eigenvalues of the Maxwell system in the presence of small changes in the interface of an inclusion. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2022080 |
| [18] |
Lixing Han. An unconstrained optimization approach for finding real eigenvalues of even order symmetric tensors. Numerical Algebra, Control and Optimization, 2013, 3 (3) : 583-599. doi: 10.3934/naco.2013.3.583 |
| [19] |
Haitao Che, Haibin Chen, Yiju Wang. On the M-eigenvalue estimation of fourth-order partially symmetric tensors. Journal of Industrial and Management Optimization, 2020, 16 (1) : 309-324. doi: 10.3934/jimo.2018153 |
| [20] |
Jun He, Guangjun Xu, Yanmin Liu. Some inequalities for the minimum M-eigenvalue of elasticity M-tensors. Journal of Industrial and Management Optimization, 2020, 16 (6) : 3035-3045. doi: 10.3934/jimo.2019092 |
2021 Impact Factor: 1.411
Tools
Metrics
Other articles
by authors
[Back to Top]