Rank-one approximation to high order tensors

Tong Zhang, Gene H. Golub

Research output: Contribution to journalArticlepeer-review

Abstract

The singular value decomposition (SVD) has been extensively used in engineering and statistical applications. This method was originally discovered by Eckart and Young in [Psychometrika, 1 (1936), pp. 211-218], where they considered the problem of low-rank approximation to a matrix. A natural generalization of the SVD is the problem of low-rank approximation to high order tensors, which we call the multidimensional SVD. In this paper, we investigate certain properties of this decomposition as well as numerical algorithms.

Original languageEnglish (US)
Pages (from-to)534-550
Number of pages17
JournalSIAM Journal on Matrix Analysis and Applications
Volume23
Issue number2
DOIs
StatePublished - 2002
Externally publishedYes

Keywords

  • Low-rank approximation
  • Singular value decomposition
  • Tensor decomposition

ASJC Scopus subject areas

  • Analysis

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