Fast Hankel tensor-vector product and its application to exponential data fitting

Weiyang Ding, Liqun Qi, Yimin Wei

Research output: Journal article publicationJournal articleAcademic researchpeer-review

37 Citations (Scopus)

Abstract

This paper is contributed to a fast algorithm for Hankel tensor-vector products. First, we explain the necessity of fast algorithms for Hankel and block Hankel tensor-vector products by sketching the algorithm for both one-dimensional and multi-dimensional exponential data fitting. For proposing the fast algorithm, we define and investigate a special class of Hankel tensors that can be diagonalized by the Fourier matrices, which is called anti-circulant tensors. Then, we obtain a fast algorithm for Hankel tensor-vector products by embedding a Hankel tensor into a larger anti-circulant tensor. The computational complexity is about O(m2nlogmn) for a square Hankel tensor of order m and dimension n, and the numerical examples also show the efficiency of this scheme. Moreover, the block version for multi-level block Hankel tensors is discussed.
Original languageEnglish
Pages (from-to)814-832
Number of pages19
JournalNumerical Linear Algebra with Applications
Volume22
Issue number5
DOIs
Publication statusPublished - 1 Jan 2015

Keywords

  • Anti-circulant tensor
  • Block Hankel tensor
  • Exponential data fitting
  • Fast Fourier transform
  • Fast tensor-vector product
  • Hankel tensor
  • Higher-order singular value decomposition

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

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