Computing Extreme Eigenvalues of Large Scale Hankel Tensors

Yannan Chen, Liqun Qi, Qun Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

22 Citations (Scopus)

Abstract

Large scale tensors, including large scale Hankel tensors, have many applications in science and engineering. In this paper, we propose an inexact curvilinear search optimization method to compute Z- and H-eigenvalues of mth order n dimensional Hankel tensors, where n is large. Owing to the fast Fourier transform, the computational cost of each iteration of the new method is about O(mnlog (mn)). Using the Cayley transform, we obtain an effective curvilinear search scheme. Then, we show that every limiting point of iterates generated by the new algorithm is an eigen-pair of Hankel tensors. Without the assumption of a second-order sufficient condition, we analyze the linear convergence rate of iterate sequence by the Kurdyka–Łojasiewicz property. Finally, numerical experiments for Hankel tensors, whose dimension may up to one million, are reported to show the efficiency of the proposed curvilinear search method.
Original languageEnglish
Pages (from-to)716-738
Number of pages23
JournalJournal of Scientific Computing
Volume68
Issue number2
DOIs
Publication statusPublished - 1 Aug 2016

Keywords

  • Cayley transform
  • Curvilinear search
  • Extreme eigenvalue
  • Fast Fourier transform
  • Hankel tensor
  • Kurdyka–Łojasiewicz property
  • Large scale tensor

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Engineering(all)
  • Computational Theory and Mathematics

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