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Best rank one approximation of real symmetric tensors can be chosen symmetric |
Shmuel FRIEDLAND( ) |
| Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60607-7045, USA |
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Abstract We show that a best rank one approximation to a real symmetric tensor, which in principle can be nonsymmetric, can be chosen symmetric. Furthermore, a symmetric best rank one approximation to a symmetric tensor is unique if the tensor does not lie on a certain real algebraic variety.
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| Keywords
Symmetric tensor
rank one approximation of tensors
uniqueness of rank one approximation
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Corresponding Author(s):
FRIEDLAND Shmuel,Email:friedlan@uic.edu
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Issue Date: 01 February 2013
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| 1 |
Chen B, He S, Li Z, Zhang S. Maximum block improvement and polynomial optimization. SIAM J Optim , 2012, 22: 87-107
doi: 10.1137/110834524
|
| 2 |
Defant A, Floret K. Tensor Norms and Operator Ideals. Amsterdam: North-Holland, 1993
|
| 3 |
Friedland S. Inverse eigenvalue problems. Linear Algebra Appl , 1977, 17: 15-51
doi: 10.1016/0024-3795(77)90039-8
|
| 4 |
Friedland S. Variation of tensor powers and spectra. Linear Multilinear Algebra , 1982, 12: 81-98
doi: 10.1080/03081088208817475
|
| 5 |
Friedland S, Robbin J, Sylvester J. On the crossing rule. Comm Pure Appl Math , 1984, 37: 19-37
doi: 10.1002/cpa.3160370104
|
| 6 |
Golub G H, Van Loan C F. Matrix Computation. 3rd ed. Baltimore: John Hopkins Univ Press, 1996
|
| 7 |
Kolda T G. On the best rank-k approximation of a symmetric tensor. Householder , 2011
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| 8 |
Lim L-H. Singular values and eigenvalues of tensors: a variational approach. In: Proc IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, (CAMSAP ’05), 1 . 2005, 129-132
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