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 journalArticlepeer-review

    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

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