2014/11/10 by Qun Wang, Wang, Qun, Guoyin Li +5 · 3 citations
Mathematics · Computer Science · Physics and Astronomy · #Tensor decomposition and applications #Matrix Theory and Algorithms #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.1411.2368
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 sum-of-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 \citeDQW1. 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.