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On sketch-and-project methods for solving tensor equations

Author

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  • Tang, Ling
  • Zhang, Yanjun
  • Li, Hanyu

Abstract

We propose a regular sketch-and-project method for solving linear tensor equations based on the t-product and present its equivalent Fourier domain version, along with several special cases corresponding to existing classical matrix equation methods. Furthermore, we extend this framework via a hierarchical approach to solve generalized Sylvester tensor equations. All the methods are proved to converge linearly in expectation. Finally, numerical experiments demonstrate the efficiency and effectiveness of the proposed approach.

Suggested Citation

  • Tang, Ling & Zhang, Yanjun & Li, Hanyu, 2026. "On sketch-and-project methods for solving tensor equations," Applied Mathematics and Computation, Elsevier, vol. 511(C).
    • Handle: RePEc:eee:apmaco:v:511:y:2026:i:c:s0096300325004606
    DOI: 10.1016/j.amc.2025.129735
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    References listed on IDEAS

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    1. Meng-Meng Zheng & Zheng-Hai Huang & Yong Wang, 2021. "T-positive semidefiniteness of third-order symmetric tensors and T-semidefinite programming," Computational Optimization and Applications, Springer, vol. 78(1), pages 239-272, January.
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