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Tensor LU and QR decompositions and their randomized algorithms

    Authors

    • Yuefeng Zhu 1
    • Yimin Wei 2

    1 School of Mathematical Sciences, Fudan University, Shanghai, P.R. China

    2 School of Mathematical Sciences and Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai, PR China

,

Document Type : Invited paper

10.52547/CMCMA.1.1.1
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Abstract

In this paper, we propose two decompositions extended from matrices to tensors, including LU and QR decompositions with their rank-revealing  and  randomized variations. We give the growth order analysis of error of the tensor QR (t-QR) and tensor LU (t-LU) decompositions. Growth order of error and running time are shown by numerical  examples. We test our methods by compressing and analyzing the image-based data, showing that the performance of tensor randomized QR decomposition is better than the tensor randomized SVD (t-rSVD) in terms of the accuracy, running time and memory.

Keywords

  • LU decomposition
  • QR decomposition
  • rank-revealing algorithm
  • randomized algorithm
  • tensor T-product
  • low-rank approximation
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Computational Mathematics and Computer Modeling with Applications (CMCMA)
Volume 1, Issue 1 - Serial Number 1
June 2022
Pages 1-16
Files
  • XML
  • PDF 1.11 M
History
  • Receive Date: 10 December 2021
  • Revise Date: 30 December 2021
  • Accept Date: 31 December 2021
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How to cite
  • RIS
  • EndNote
  • Mendeley
  • BibTeX
  • APA
  • MLA
  • HARVARD
  • CHICAGO
  • VANCOUVER
Statistics
  • Article View: 881
  • PDF Download: 1,468

APA

Zhu, Y. and Wei, Y. (2022). Tensor LU and QR decompositions and their randomized algorithms. Computational Mathematics and Computer Modeling with Applications (CMCMA), 1(1), 1-16. doi: 10.52547/CMCMA.1.1.1

MLA

Zhu, Y. , and Wei, Y. . "Tensor LU and QR decompositions and their randomized algorithms", Computational Mathematics and Computer Modeling with Applications (CMCMA), 1, 1, 2022, 1-16. doi: 10.52547/CMCMA.1.1.1

HARVARD

Zhu, Y., Wei, Y. (2022). 'Tensor LU and QR decompositions and their randomized algorithms', Computational Mathematics and Computer Modeling with Applications (CMCMA), 1(1), pp. 1-16. doi: 10.52547/CMCMA.1.1.1

CHICAGO

Y. Zhu and Y. Wei, "Tensor LU and QR decompositions and their randomized algorithms," Computational Mathematics and Computer Modeling with Applications (CMCMA), 1 1 (2022): 1-16, doi: 10.52547/CMCMA.1.1.1

VANCOUVER

Zhu, Y., Wei, Y. Tensor LU and QR decompositions and their randomized algorithms. Computational Mathematics and Computer Modeling with Applications (CMCMA), 2022; 1(1): 1-16. doi: 10.52547/CMCMA.1.1.1

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