Best rank one approximation of real symmetric tensors can be chosen symmetric

Shmuel Friedland

doi:10.1007/s11464-012-0262-x

Front. Math. China ›› 2012, Vol. 8 ›› Issue (1) : 19 -40. DOI: 10.1007/s11464-012-0262-x

Research Article

RESEARCH ARTICLE

Best rank one approximation of real symmetric tensors can be chosen symmetric

Shmuel Friedland ¹^,^a

Author information +

History +

PDF (186KB)

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.

Keywords

Symmetric tensor / rank one approximation of tensors / uniqueness of rank one approximation

Cite this article

Download citation ▾

Shmuel Friedland. Best rank one approximation of real symmetric tensors can be chosen symmetric. Front. Math. China, 2012, 8(1): 19-40 DOI:10.1007/s11464-012-0262-x

登录浏览全文

4963

注册一个新账户忘记密码

References

Publishing order | Descend order by publishing year | Descend order by cited within

[1]	Chen B., He S., Li Z., Zhang S.. Maximum block improvement and polynomial optimization. SIAM J Optim, 2012, 22: 87-107

[2]	Defant A., Floret K.. Tensor Norms and Operator Ideals, 1993, Amsterdam: North-Holland

[3]	Friedland S.. Inverse eigenvalue problems. Linear Algebra Appl, 1977, 17: 15-51

[4]	Friedland S.. Variation of tensor powers and spectra. Linear Multilinear Algebra, 1982, 12: 81-98

[5]	Friedland S., Robbin J., Sylvester J.. On the crossing rule. Comm Pure Appl Math, 1984, 37: 19-37

[6]	Golub G. H., Van Loan C. F.. Matrix Computation, 1996 3rd ed. Baltimore: John Hopkins Univ Press

[7]	Kolda T G. On the best rank-k approximation of a symmetric tensor. Householder, 2011

[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