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Some results on $l^k$-eigenvalues of tensor and related spectral radius
1. | School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China |
2. | Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong |
References:
[1] |
L. Bloy and R. Verma, On computing the underlying fiber directions from the diffusion orientation distribution function, in "Medical Image Computing and Computer-Assisted Intervention MICCAI 2008'' (eds. Dimitris Metaxas, Leon Axel, Gabor Fichtinger and Gábor Székely), Springer-Verlag, Berlin/Heidelberg, (2008), 1-8. |
[2] |
K. C. Chang, K. Pearson and T. Zhang, Perron Frobenius theorem for nonnegative tensors, Commu Math Sci, 6 (2008), 507-520. |
[3] |
K. C. Chang, L. Qi and G. Zhou, Singular values of a real rectangular tensor, J. Math. Anal. Appl., 370 (2010), 284-294.
doi: 10.1016/j.jmaa.2010.04.037. |
[4] |
L. H. Lim, Singular values and eigenvalues of tensors: a variational approach, in "Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Addaptive Processing, CAMSAP'05'', 1, IEEE Computer Society Press, Piscataway, (2005), 129-132. |
[5] |
M. Ng, L. Qi and G. Zhou, Finding the largest eigenvalue of a non-negative tensor, SIAM J. Matrix Anal. Appl., 31 (2009), 1090-1099.
doi: 10.1137/09074838X. |
[6] |
L. Qi, Eigenvalues of a real supersymmetric tensor, J. Symbolic Comput., 40 (2005), 1302-1324.
doi: 10.1016/j.jsc.2005.05.007. |
[7] |
L. Qi, F. Wang and Y. Wang, Z-eigenvalue methods for a global polynomial optimization problem, Math. Program., 118 (2009), 301-316.
doi: 10.1007/s10107-007-0193-6. |
[8] |
L. Qi, G. Yu and E. X. Wu, Higher order positive semi-definite diffusion tensor imaging, SIAM J. Imaging Sci., 3 (2010), 416-433. |
[9] |
Y. 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. |
show all references
References:
[1] |
L. Bloy and R. Verma, On computing the underlying fiber directions from the diffusion orientation distribution function, in "Medical Image Computing and Computer-Assisted Intervention MICCAI 2008'' (eds. Dimitris Metaxas, Leon Axel, Gabor Fichtinger and Gábor Székely), Springer-Verlag, Berlin/Heidelberg, (2008), 1-8. |
[2] |
K. C. Chang, K. Pearson and T. Zhang, Perron Frobenius theorem for nonnegative tensors, Commu Math Sci, 6 (2008), 507-520. |
[3] |
K. C. Chang, L. Qi and G. Zhou, Singular values of a real rectangular tensor, J. Math. Anal. Appl., 370 (2010), 284-294.
doi: 10.1016/j.jmaa.2010.04.037. |
[4] |
L. H. Lim, Singular values and eigenvalues of tensors: a variational approach, in "Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Addaptive Processing, CAMSAP'05'', 1, IEEE Computer Society Press, Piscataway, (2005), 129-132. |
[5] |
M. Ng, L. Qi and G. Zhou, Finding the largest eigenvalue of a non-negative tensor, SIAM J. Matrix Anal. Appl., 31 (2009), 1090-1099.
doi: 10.1137/09074838X. |
[6] |
L. Qi, Eigenvalues of a real supersymmetric tensor, J. Symbolic Comput., 40 (2005), 1302-1324.
doi: 10.1016/j.jsc.2005.05.007. |
[7] |
L. Qi, F. Wang and Y. Wang, Z-eigenvalue methods for a global polynomial optimization problem, Math. Program., 118 (2009), 301-316.
doi: 10.1007/s10107-007-0193-6. |
[8] |
L. Qi, G. Yu and E. X. Wu, Higher order positive semi-definite diffusion tensor imaging, SIAM J. Imaging Sci., 3 (2010), 416-433. |
[9] |
Y. 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. |
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