Citation: |
[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. |