New classes of positive semi-definite Hankel tensors

Qun Wang, Guoyin Li, Liqun Qi, Yi Xu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)231-248
Number of pages18
JournalMinimax Theory and its Applications
Volume2
Issue number2
Publication statusPublished - 1 Jan 2017

Keywords

  • Generating vectors
  • Hankel tensors
  • Positive semi-definiteness
  • Strong Hankel tensors

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Control and Optimization

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