The best rank-1 approximation of a symmetric tensor and related spherical optimization problems

Xinzhen Zhang, Chen Ling, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

57 Citations (Scopus)


In this paper, we show that for a symmetric tensor, its best symmetric rank-1 approximation is its best rank-1 approximation. Based on this result, a positive lower bound for the best rank-1 approximation ratio of a symmetric tensor is given. Furthermore, a higher order polynomial spherical optimization problem can be reformulated as a multilinear spherical optimization problem. Then, we present a modified power algorithm for solving the homogeneous polynomial spherical optimization problem. Numerical results are presented, illustrating the effectiveness of the proposed algorithm.
Original languageEnglish
Pages (from-to)806-821
Number of pages16
JournalSIAM Journal on Matrix Analysis and Applications
Issue number3
Publication statusPublished - 16 Oct 2012


  • Power algorithm
  • Symmetric tensor
  • The best rank-1 approximation
  • The best symmetric rank-1 approximation

ASJC Scopus subject areas

  • Analysis

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