References
- B.W. Bader and T.G. Kolda and others, MATLAB Tensor Toolbox, Version 3.0, 2018. Available at https://www.tensortoolbox.org.
- S.R. Bulo and M. Pelillo, A generalization of the Motzkin–Straus theorem to hypergraphs, Optim. Lett. 3 (2009), pp. 187–198. doi: 10.1007/s11590-008-0100-y
- K.C. Chang, K. Pearson and T. Zhang, Perron–Frobenius theorem for nonnegative tensors, Commu. Math. Sci. 6(2) (2008), pp. 507–520. doi: 10.4310/CMS.2008.v6.n2.a12
- K.C. Chang, K. Pearson and T. Zhang, On eigenvalue problems of real symmetric tensors, J. Math. Anal. Appl. 350 (2009), pp. 416–422. doi: 10.1016/j.jmaa.2008.09.067
- K.C. Chang, K. Pearson and T. Zhang, Some variational principles of the Z-eigenvalues for nonnegative tensors, Linear Algebra Appl. 438 (2013), pp. 4166–4182. doi: 10.1016/j.laa.2013.02.013
- K.C. Chang and T. Zhang, On the uniqueness and nonuniqueness of the Z-eigenvector for transition probability tensors, J. Math. Anal. Appl. 408 (2013), pp. 525–540. doi: 10.1016/j.jmaa.2013.04.019
- L. De Lathauwer, B. De Moor and J. Vandewalle, On the best rank-1 and rank-(R1, R2, RN) approximation of higher-order tensors, SIAM J. Matrix Anal. Appl. 21 (2000), pp. 1324–1342. doi: 10.1137/S0895479898346995
- J.E. Dennis Jr. and J.J. More, Quasi-Newton methods, motivation and theory, SIAM Rev. 19 (1977), pp. 46–89. doi: 10.1137/1019005
- E. Kofidis and P.A. Regalia, On the best rank-1 approximation of higher-order supersymmetric tensors, SIAM J. Matrix Anal. Appl. 23 (2002), pp. 863–884. doi: 10.1137/S0895479801387413
- T.G. Kolda and J.R. Mayo, Shifted power method for computing tensor eigenpairs, SIAM J. Matrix Anal. Appl. 32 (2011), pp. 1095–1124. doi: 10.1137/100801482
- T.G. Kolda and J.R. Mayo, An adaptive shifted power methods for computing generalized tensor eigenpairs, SIAM J. Matrix Anal. Appl. 35 (2014), pp. 1563–1581. doi: 10.1137/140951758
- G. Li, L. Qi and G. Yu, The Z-eigenvalues of a symmetric tensor and its application to spectral hypergraph theory, Numer. Linear Algebra Appl. 20 (2013), pp. 1001–1029. doi: 10.1002/nla.1877
- L.H. Lim, Singular values and eigenvalues of tensors: A variational approach, Proceedings of 1st IEEE International Workshop on Computational Advances of Multi-tensor Adaptive Processing, 2005, pp. 129–132.
- M. Ng, L. Qi and G. Zhou, Finding the largest eigenvalue of a non-negative tensor, SIAM J. Matrix Anal. Appl. 31 (2009), pp. 1090–1099. doi: 10.1137/09074838X
- Q. Ni, L. Qi and F. Wang, An eigenvalue method for testing positive definiteness of a multivariate form, IEEE Trans. Autom. Control 53 (2008), pp. 1096–1107. doi: 10.1109/TAC.2008.923679
- Q. Ni and L. Qi, A quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map, J. Glob. Optim. 61 (2015), pp. 627–641. doi: 10.1007/s10898-014-0209-8
- J. Nocedal and S.J. Wright, Numerical Optimization, Springer, New York, 1999.
- L. Qi, Eigenvalues of a real supersymmetric tensor, J. Symb. Comput. 40 (2005), pp. 1302–1324. doi: 10.1016/j.jsc.2005.05.007
- L. Qi and K.L. Teo, Multivariate polynomial minimization and its application in signal processing, J. Global Optim. 46 (2003), pp. 419–433. doi: 10.1023/A:1024778309049
- L. Qi, F. Wang and Y. Wang, Z-eigenvalue methods for a global polynomial optimization problems, Math. Program. 118 (2009), pp. 301–316. doi: 10.1007/s10107-007-0193-6
- L. Qi, G. Yu and E.X. Wu, Higher order positive semi-definite diffusion tensor imaging, SIAM J. Imaging Sci. 3 (2010), pp. 416–433. doi: 10.1137/090755138
- W. Yang and Q. Ni, A cubically convergent method for solving the largest eigenvalue of a nonnegative irreducible tensor, Numer. Algor. 77(4) (2018), pp. 1183–1197. doi: 10.1007/s11075-017-0358-1
- M. Zeng and Q. Ni, Quasi-Newton method for computing Z-eigenpairs of a symmetric tensor, Pacific J. Optim. 2 (2015), pp. 279–290.