-
Previous Article
On a risk model with randomized dividend-decision times
- JIMO Home
- This Issue
-
Next Article
A power penalty method for the general traffic assignment problem with elastic demand
Bounds for the greatest eigenvalue of positive tensors
1. | Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, China, China |
References:
[1] |
S. R. Bulò and M. Pelillo, A generalization of the Motzkin-Straus theorem to hypergraphs, Optim. Lett., 3 (2009), 187-295.
doi: 10.1007/s11590-008-0108-3. |
[2] |
S. R. Bulò and M. Pelillo, New bounds on the clique number of graphs based on spectral hypergraph theory, in Learning and Intelligent Optimization, (ed. T. Stützle), Springer Verlag, Berlin, (2009), 45-48. |
[3] |
K. C. Chang, K. Pearson and T. Zhang, On eigenvalue problems of real symmetric tensors, J. Math. Anal. Appl., 350 (2009), 416-422.
doi: 10.1016/j.jmaa.2008.09.067. |
[4] |
K. C. Chang, K. Pearson and T. Zhang, Perron Frobenius theorem for nonnegative tensors, Comm. Math. Sci., 6 (2008), 507-520.
doi: 10.4310/CMS.2008.v6.n2.a12. |
[5] |
L. Collatz, Einschliessungssatz die charakteristischen Zahlen von Matrizen, Math. Zeit., 48 (1942), 221-226.
doi: 10.1007/BF01180013. |
[6] |
J. Cooper and A. Dutle, Spectra of uniform hypergraphs, Department of Mathematics, University of South Carolina, June 2011, Arxiv preprint arXiv:1106.4856, (2011).
doi: 10.1016/j.laa.2011.11.018. |
[7] |
P. Drineas and L. H. Lim, A Multilinear Spectral Theory of Hyper-Graphs and Expander Hypergraphs,, 2005., ().
|
[8] |
S. Friedland, S. Gaubert and L. Han, Perron-Frobenius theorem for nonnegative multilinear forms and extensions, to appear in Linear Algebra and Its Applications, 438 (2013), 738-749.
doi: 10.1016/j.laa.2011.02.042. |
[9] |
S. Hu and L. Qi, Algebraic connectivity of an even uniform hypergraph, Journal of Combinatorial Optimization, 24 (2012), 564-579.
doi: 10.1007/s10878-011-9407-1. |
[10] |
W. Li and M. Ng, Existence and Uniqueness of Stationary Probability Vector of a Transition Probability Tensor, Technical report, Department of Mathematics, The Hong Kong Baptist University, 2011. |
[11] |
L. H. Lim, Multilinear Pagerank: Measuring Higher Order Connectivity in Linked Objects, The internet: Today and Tomorrow, 2005. |
[12] |
L. H. Lim, Singular values and eigenvalues of tensors: A variational approach, in Proceedings of the First IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), (2005), 129-132. |
[13] |
Y. Liu, G. Zhou and N. F. Ibrahim, An always convergent algorithm for the largest eigenvalue of an irreducible nonnegative tensor, Journal of Computational and Applied Mathematics, 235 (2010), 286-292.
doi: 10.1016/j.cam.2010.06.002. |
[14] |
H. Minc, Nonnegative Matrices, New York: John Wiley and Sons, Inc, 1988. |
[15] |
M. Ng, L. Qi and G. Zhou, Finding the largest eigenvalue of a nonnegative tensor, SIAM J. Matrix Anal. Appl., 31 (2009), 1090-1099.
doi: 10.1137/09074838X. |
[16] |
L. Qi, Eigenvalues of a real supersymmetric tensor, J. Symbolic Comput., 40 (2005), 1302-1324.
doi: 10.1016/j.jsc.2005.05.007. |
[17] |
L. Qi, Eigenvalue and invariants of a tensor, J. Math. Anal. Appl., 325 (2007), 1363-1377.
doi: 10.1016/j.jmaa.2006.02.071. |
[18] |
L. Qi, W. Sun and Y. Wang, Numerical multilinear algebra and its applications, Front. Math. China, 2 (2007), 501-526.
doi: 10.1007/s11464-007-0031-4. |
[19] |
Y. N. Yang and Q. Z. Yang, Further results for Perron-Frobenius theorem for nonnegative tensors, SIAM. J. Matrix Anal. Appl., 31 (2010), 2517-2530.
doi: 10.1137/090778766. |
[20] |
Y. N. Yang, Q. Z. Yang and Y. G. Li, An algorithm to find the spectral radius of nonnegative tensors and its convergence analysis, arXiv:1102.2668, (2011). |
[21] |
F. X. Zhang, The smoothing method for finding the largest eigenvalue of nonnegative matrices, Numerical Mathematics: A Journal of Chinese Universities, 23 (2001), 45-55, Chinese Series. |
[22] |
L. Zhang and L. Qi, Linear convergence of an algorithm for computing the largest eigenvalue of a nonnegative tensor, Numercal Linear Algebra with Applications, 19 (2012), 830-841.
doi: 10.1002/nla.822. |
show all references
References:
[1] |
S. R. Bulò and M. Pelillo, A generalization of the Motzkin-Straus theorem to hypergraphs, Optim. Lett., 3 (2009), 187-295.
doi: 10.1007/s11590-008-0108-3. |
[2] |
S. R. Bulò and M. Pelillo, New bounds on the clique number of graphs based on spectral hypergraph theory, in Learning and Intelligent Optimization, (ed. T. Stützle), Springer Verlag, Berlin, (2009), 45-48. |
[3] |
K. C. Chang, K. Pearson and T. Zhang, On eigenvalue problems of real symmetric tensors, J. Math. Anal. Appl., 350 (2009), 416-422.
doi: 10.1016/j.jmaa.2008.09.067. |
[4] |
K. C. Chang, K. Pearson and T. Zhang, Perron Frobenius theorem for nonnegative tensors, Comm. Math. Sci., 6 (2008), 507-520.
doi: 10.4310/CMS.2008.v6.n2.a12. |
[5] |
L. Collatz, Einschliessungssatz die charakteristischen Zahlen von Matrizen, Math. Zeit., 48 (1942), 221-226.
doi: 10.1007/BF01180013. |
[6] |
J. Cooper and A. Dutle, Spectra of uniform hypergraphs, Department of Mathematics, University of South Carolina, June 2011, Arxiv preprint arXiv:1106.4856, (2011).
doi: 10.1016/j.laa.2011.11.018. |
[7] |
P. Drineas and L. H. Lim, A Multilinear Spectral Theory of Hyper-Graphs and Expander Hypergraphs,, 2005., ().
|
[8] |
S. Friedland, S. Gaubert and L. Han, Perron-Frobenius theorem for nonnegative multilinear forms and extensions, to appear in Linear Algebra and Its Applications, 438 (2013), 738-749.
doi: 10.1016/j.laa.2011.02.042. |
[9] |
S. Hu and L. Qi, Algebraic connectivity of an even uniform hypergraph, Journal of Combinatorial Optimization, 24 (2012), 564-579.
doi: 10.1007/s10878-011-9407-1. |
[10] |
W. Li and M. Ng, Existence and Uniqueness of Stationary Probability Vector of a Transition Probability Tensor, Technical report, Department of Mathematics, The Hong Kong Baptist University, 2011. |
[11] |
L. H. Lim, Multilinear Pagerank: Measuring Higher Order Connectivity in Linked Objects, The internet: Today and Tomorrow, 2005. |
[12] |
L. H. Lim, Singular values and eigenvalues of tensors: A variational approach, in Proceedings of the First IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), (2005), 129-132. |
[13] |
Y. Liu, G. Zhou and N. F. Ibrahim, An always convergent algorithm for the largest eigenvalue of an irreducible nonnegative tensor, Journal of Computational and Applied Mathematics, 235 (2010), 286-292.
doi: 10.1016/j.cam.2010.06.002. |
[14] |
H. Minc, Nonnegative Matrices, New York: John Wiley and Sons, Inc, 1988. |
[15] |
M. Ng, L. Qi and G. Zhou, Finding the largest eigenvalue of a nonnegative tensor, SIAM J. Matrix Anal. Appl., 31 (2009), 1090-1099.
doi: 10.1137/09074838X. |
[16] |
L. Qi, Eigenvalues of a real supersymmetric tensor, J. Symbolic Comput., 40 (2005), 1302-1324.
doi: 10.1016/j.jsc.2005.05.007. |
[17] |
L. Qi, Eigenvalue and invariants of a tensor, J. Math. Anal. Appl., 325 (2007), 1363-1377.
doi: 10.1016/j.jmaa.2006.02.071. |
[18] |
L. Qi, W. Sun and Y. Wang, Numerical multilinear algebra and its applications, Front. Math. China, 2 (2007), 501-526.
doi: 10.1007/s11464-007-0031-4. |
[19] |
Y. N. Yang and Q. Z. Yang, Further results for Perron-Frobenius theorem for nonnegative tensors, SIAM. J. Matrix Anal. Appl., 31 (2010), 2517-2530.
doi: 10.1137/090778766. |
[20] |
Y. N. Yang, Q. Z. Yang and Y. G. Li, An algorithm to find the spectral radius of nonnegative tensors and its convergence analysis, arXiv:1102.2668, (2011). |
[21] |
F. X. Zhang, The smoothing method for finding the largest eigenvalue of nonnegative matrices, Numerical Mathematics: A Journal of Chinese Universities, 23 (2001), 45-55, Chinese Series. |
[22] |
L. Zhang and L. Qi, Linear convergence of an algorithm for computing the largest eigenvalue of a nonnegative tensor, Numercal Linear Algebra with Applications, 19 (2012), 830-841.
doi: 10.1002/nla.822. |
[1] |
Stefan Klus, Péter Koltai, Christof Schütte. On the numerical approximation of the Perron-Frobenius and Koopman operator. Journal of Computational Dynamics, 2016, 3 (1) : 51-79. doi: 10.3934/jcd.2016003 |
[2] |
Stefan Klus, Christof Schütte. Towards tensor-based methods for the numerical approximation of the Perron--Frobenius and Koopman operator. Journal of Computational Dynamics, 2016, 3 (2) : 139-161. doi: 10.3934/jcd.2016007 |
[3] |
Martin Lustig, Caglar Uyanik. Perron-Frobenius theory and frequency convergence for reducible substitutions. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 355-385. doi: 10.3934/dcds.2017015 |
[4] |
Gary Froyland, Ognjen Stancevic. Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - B, 2010, 14 (2) : 457-472. doi: 10.3934/dcdsb.2010.14.457 |
[5] |
Marianne Akian, Stéphane Gaubert, Antoine Hochart. A game theory approach to the existence and uniqueness of nonlinear Perron-Frobenius eigenvectors. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 207-231. doi: 10.3934/dcds.2020009 |
[6] |
Wen Li, Wei-Hui Liu, Seak Weng Vong. Perron vector analysis for irreducible nonnegative tensors and its applications. Journal of Industrial and Management Optimization, 2021, 17 (1) : 29-50. doi: 10.3934/jimo.2019097 |
[7] |
Ruixue Zhao, Jinyan Fan. Quadratic tensor eigenvalue complementarity problems. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022073 |
[8] |
King Hann Lim, Hong Hui Tan, Hendra G. Harno. Approximate greatest descent in neural network optimization. Numerical Algebra, Control and Optimization, 2018, 8 (3) : 327-336. doi: 10.3934/naco.2018021 |
[9] |
Marc Kesseböhmer, Sabrina Kombrink. A complex Ruelle-Perron-Frobenius theorem for infinite Markov shifts with applications to renewal theory. Discrete and Continuous Dynamical Systems - S, 2017, 10 (2) : 335-352. doi: 10.3934/dcdss.2017016 |
[10] |
Wanbin Tong, Hongjin He, Chen Ling, Liqun Qi. A nonmonotone spectral projected gradient method for tensor eigenvalue complementarity problems. Numerical Algebra, Control and Optimization, 2020, 10 (4) : 425-437. doi: 10.3934/naco.2020042 |
[11] |
Venkateswaran P. Krishnan, Plamen Stefanov. A support theorem for the geodesic ray transform of symmetric tensor fields. Inverse Problems and Imaging, 2009, 3 (3) : 453-464. doi: 10.3934/ipi.2009.3.453 |
[12] |
Fan Wu. Conditional regularity for the 3D Navier-Stokes equations in terms of the middle eigenvalue of the strain tensor. Evolution Equations and Control Theory, 2021, 10 (3) : 511-518. doi: 10.3934/eect.2020078 |
[13] |
Ya Li, ShouQiang Du, YuanYuan Chen. Modified spectral PRP conjugate gradient method for solving tensor eigenvalue complementarity problems. Journal of Industrial and Management Optimization, 2022, 18 (1) : 157-172. doi: 10.3934/jimo.2020147 |
[14] |
Jan Boman, Vladimir Sharafutdinov. Stability estimates in tensor tomography. Inverse Problems and Imaging, 2018, 12 (5) : 1245-1262. doi: 10.3934/ipi.2018052 |
[15] |
Shenglong Hu. A note on the solvability of a tensor equation. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021146 |
[16] |
M. S. Lee, B. S. Goh, H. G. Harno, K. H. Lim. On a two-phase approximate greatest descent method for nonlinear optimization with equality constraints. Numerical Algebra, Control and Optimization, 2018, 8 (3) : 315-326. doi: 10.3934/naco.2018020 |
[17] |
Meng Ding, Ting-Zhu Huang, Xi-Le Zhao, Michael K. Ng, Tian-Hui Ma. Tensor train rank minimization with nonlocal self-similarity for tensor completion. Inverse Problems and Imaging, 2021, 15 (3) : 475-498. doi: 10.3934/ipi.2021001 |
[18] |
Mengmeng Zheng, Ying Zhang, Zheng-Hai Huang. Global error bounds for the tensor complementarity problem with a P-tensor. Journal of Industrial and Management Optimization, 2019, 15 (2) : 933-946. doi: 10.3934/jimo.2018078 |
[19] |
Yiju Wang, Guanglu Zhou, Louis Caccetta. Nonsingular $H$-tensor and its criteria. Journal of Industrial and Management Optimization, 2016, 12 (4) : 1173-1186. doi: 10.3934/jimo.2016.12.1173 |
[20] |
Hirofumi Notsu, Masato Kimura. Symmetry and positive definiteness of the tensor-valued spring constant derived from P1-FEM for the equations of linear elasticity. Networks and Heterogeneous Media, 2014, 9 (4) : 617-634. doi: 10.3934/nhm.2014.9.617 |
2020 Impact Factor: 1.801
Tools
Metrics
Other articles
by authors
[Back to Top]