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

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

Research output: Contribution to journalArticle

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
JournalSIAM Journal on Scientific Computing
Volume34
Issue number1
DOIs
Publication statusPublished - 28 May 2012

Keywords

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

Fingerprint Dive into the research topics of 'Wedderburn rank reduction and Krylov subspace method for tensor approximation. Part 1: Tucker case'. Together they form a unique fingerprint.

Cite this