An Efficient Randomized Algorithm for Computing the Approximate Tucker Decomposition

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Original languageEnglish
Article number32
Journal / PublicationJournal of Scientific Computing
Issue number2
Online published17 Jun 2021
Publication statusPublished - Aug 2021


By combining the thin QR decomposition and the subsampled randomized Fourier transform (SRFT), we obtain an efficient randomized algorithm for computing the approximate Tucker decomposition with a given target multilinear rank. We also combine this randomized algorithm with the power iteration technique to improve the efficiency of the algorithm. By using the results about the singular values of the product of orthonormal matrices with the Kronecker product of SRFT matrices, we obtain the error bounds of these two algorithms. Finally, the efficiency of these algorithms is illustrated by several numerical examples.

Research Area(s)

  • Approximate Tucker decomposition, Dimension reduction maps, Power iteration technique, Random projection, Randomized algorithms, Subsampled randomized Fourier transform, Thin QR decomposition