Wedderburn rank reduction and Krylov subspace method for tensor approximation. Part 1: Tucker case

S. A. Goreinov, I. V. Oseledets, D. V. Savostyanov

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14 Citations (Scopus)

Abstract

New algorithms are proposed for the Tucker approximation of a 3-tensor accessed only through a tensor-by-vector-by-vector multiplication subroutine. In the matrix case, the Krylov methods are methods of choice to approximate the dominant column and row subspaces of a sparse or structured matrix given through a matrix-by-vector operation. Using the Wedderburn rank reduction formula, we propose a matrix approximation algorithm that computes the Krylov subspaces and can be generalized to 3-tensors. The numerical experiments show that on quantum chemistry data the proposed tensor methods outperform the minimal Krylov recursion of Savas and Eldén.

Original languageEnglish
Pages (from-to)A1-A27
JournalSIAM Journal on Scientific Computing
Volume34
Issue number1
DOIs
Publication statusPublished - 2012
Externally publishedYes

Keywords

  • Fast compression
  • Krylov subspace methods
  • Multidimensional arrays
  • Sparse tensors
  • Structured tensors
  • Tucker approximation
  • Wedderburn rank reduction

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