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<p>Efficiently solving tensor linear systems plays a critical role in many high-dimensional applications, such as image reconstruction, video analysis, and medical imaging. In this paper, we introduce two novel methods: the Tensor Sampling Kaczmarz-Motzkin (TSKM) method and its Fourier-transformed variant (FTSKM). The TSKM method combines random sampling with greedy strategies to achieve faster convergence than the traditional Tensor Randomized Kaczmarz (TRK) method. The FTSKM method further enhances computational efficiency by utilizing matrix operations in the Fourier domain. Theoretical analysis establishes the convergence of both algorithms. Numerical experiments demonstrate significant reductions in the number of iterations and CPU time compared to the TRK method. In particular, the FTSKM method achieves superior computational efficiency, making it highly suitable for large-scale tensor problems.</p>

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A sampling Kaczmarz-Motzkin algorithm for tensor linear systems

  • 期刊论文

  • 发表日期：

    2025年7月18日

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  • Yu-Qi Niu,
  • Susu Yin,
  • Peng Lv

摘要

Efficiently solving tensor linear systems plays a critical role in many high-dimensional applications, such as image reconstruction, video analysis, and medical imaging. In this paper, we introduce two novel methods: the Tensor Sampling Kaczmarz-Motzkin (TSKM) method and its Fourier-transformed variant (FTSKM). The TSKM method combines random sampling with greedy strategies to achieve faster convergence than the traditional Tensor Randomized Kaczmarz (TRK) method. The FTSKM method further enhances computational efficiency by utilizing matrix operations in the Fourier domain. Theoretical analysis establishes the convergence of both algorithms. Numerical experiments demonstrate significant reductions in the number of iterations and CPU time compared to the TRK method. In particular, the FTSKM method achieves superior computational efficiency, making it highly suitable for large-scale tensor problems.