An Efficient Randomized Algorithm for Computing the Approximate Tucker Decomposition

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 techn...

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Vydáno v:Journal of scientific computing Ročník 88; číslo 2; s. 32
Hlavní autoři: Che, Maolin, Wei, Yimin, Yan, Hong
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.08.2021
Springer Nature B.V
Témata:
Algorithms
Approximation
Computation
Computational Mathematics and Numerical Analysis
Decomposition
Fourier transforms
Iterative methods
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Random variables
Theoretical
Subsampled randomized Fourier transform
65F10
Power iteration technique
Dimension reduction maps
Randomized algorithms
Thin QR decomposition
65F15
Random projection
Approximate Tucker decomposition
15A69
15A18
ISSN:0885-7474, 1573-7691
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Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-021-01545-5