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Slice tensor splitting method for solving tensor equation

Author

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  • Jiang, Zhuling
  • Li, Jicheng

Abstract

Firstly, we define an (r,r,⋯,r)-slice tensor, and then solve an (r,r,⋯,r)-slice tensor equation by direct method. Secondly, we propose a new splitting of the coefficient tensor to develop a slice tensor splitting method, which is different from the tensor splitting methods in [1,2]. At each iteration of this method, an (r,r,⋯,r)-slice tensor equation is solved. Finally, we prove the local convergence of the proposed method under appropriate conditions, and give numerical experiments to illustrate the effectiveness of this method.

Suggested Citation

  • Jiang, Zhuling & Li, Jicheng, 2024. "Slice tensor splitting method for solving tensor equation," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    • Handle: RePEc:eee:apmaco:v:463:y:2024:i:c:s0096300323005362
    DOI: 10.1016/j.amc.2023.128367
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    References listed on IDEAS

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    1. Yisheng Song & Gaohang Yu, 2016. "Properties of Solution Set of Tensor Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 85-96, July.
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