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Randomized Average Kaczmarz Algorithm for Tensor Linear Systems

Author

Listed:
  • Wendi Bao

    (College of Science, China University of Petroleum, Qingdao 266580, China)

  • Feiyu Zhang

    (College of Science, China University of Petroleum, Qingdao 266580, China)

  • Weiguo Li

    (College of Science, China University of Petroleum, Qingdao 266580, China)

  • Qin Wang

    (College of Science, China University of Petroleum, Qingdao 266580, China)

  • Ying Gao

    (College of Science, China University of Petroleum, Qingdao 266580, China)

Abstract

For solving tensor linear systems under the tensor–tensor t-product, we propose the randomized average Kaczmarz (TRAK) algorithm, the randomized average Kaczmarz algorithm with random sampling (TRAKS), and their Fourier version, which can be effectively implemented in a distributed environment. We analyzed the relationships (of the updated formulas) between the original algorithms and their Fourier versions in detail and prove that these new algorithms can converge to the unique least F-norm solution of the consistent tensor linear systems. Extensive numerical experiments show that they significantly outperform the tensor-randomized Kaczmarz (TRK) algorithm in terms of both iteration counts and computing times and have potential in real-world data, such as video data, CT data, etc.

Suggested Citation

  • Wendi Bao & Feiyu Zhang & Weiguo Li & Qin Wang & Ying Gao, 2022. "Randomized Average Kaczmarz Algorithm for Tensor Linear Systems," Mathematics, MDPI, vol. 10(23), pages 1-24, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4594-:d:993070
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    References listed on IDEAS

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    1. Carlton, Matthew A., 2008. "Probability and Statistics for Computer Scientists," The American Statistician, American Statistical Association, vol. 62, pages 271-272, August.
    2. Hua Zhou & Lexin Li & Hongtu Zhu, 2013. "Tensor Regression with Applications in Neuroimaging Data Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 540-552, June.
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    Cited by:

    1. Xuezhong Wang & Ping Wei & Yimin Wei, 2023. "A Fixed Point Iterative Method for Third-order Tensor Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 334-357, April.

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