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Title: New classes of positive semi-definite hankel tensors
Authors: Wang, Q
Li, GY
Qi, LQ 
Xu, Y
Keywords: Hankel tensors
Generating vectors
Positive semi
Strong Hankel tensors
Issue Date: 2017
Publisher: Heldermann Verlag
Source: Minimax theory and its applications, 2017, v. 2, no. 2, p. 231-248 How to cite?
Journal: Minimax theory and its applications 
Abstract: A Hankel tensor is called a strong Hankel tensor if the Hankel matrix generated by its generating vector is positive semi-definite. It is known that an even order strong Hankel tensor is a sumof- squares tensor, and thus a positive semi-definite tensor. The SOS decomposition of strong Hankel tensors has been well-studied by Ding, Qi and Wei [11]. On the other hand, very little is known for positive semi-definite Hankel tensors which are not strong Hankel tensors. In this paper, we study some classes of positive semi-definite Hankel tensors which are not strong Hankel tensors. These include truncated Hankel tensors and quasi-truncated Hankel tensors. Then we show that a strong Hankel tensor generated by an absoluate integrable function is always completely decomposable, and give a class of SOS Hankel tensors which are not completely decomposable.
ISSN: 2199-1413
EISSN: 2199-1421
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