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Title: Positive semi-definiteness of generalized anti-circulant tensors
Authors: Li, G
Qi, L 
Wang, Q
Keywords: Anti-circulant tensors
Circulant index
Generalized anti-circulant tensor
Generating vectors
Positive semi-definiteness
Issue Date: 2016
Publisher: International Press
Source: Communications in mathematical sciences, 2016, v. 14, no. 4, p. 941-952 How to cite?
Journal: Communications in mathematical sciences 
Abstract: Anti-circulant tensors have applications in exponential data fitting. They are special Hankel tensors. In this paper, we extend the definition of anti-circulant tensors to generalized anticirculant tensors by introducing a circulant index r such that the entries of the generating vector of a Hankel tensor are circulant with module r. In the special case when r=n, where n is the dimension of the Hankel tensor, the generalized anti-circulant tensor reduces to the anti-circulant tensor. Hence, generalized anti-circulant tensors are still special Hankel tensors. For the cases that GCD(m,r)=1, GCD(m,r)=2, and some other cases, including the matrix case that m=2, we give necessary and sufficient conditions for positive semi-definiteness of even-order generalized anti-circulant tensors and show that, in these cases, they are sum-of-squares tensors. This shows that, in these cases, there are no PNS (positive semi-definite tensors which are not sum-of-squares) Hankel tensors.
ISSN: 1539-6746 (print)
1945-0796 (online)
DOI: 10.4310/CMS.2016.v14.n4.a3
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