Abstract
In this paper, we propose a new preconditioned SOR method for solving the multi-linear systems whose coefficient tensor is an \({\mathcal{M}}\)-tensor. The corresponding comparison for spectral radii of iterative tensors is given. Numerical examples demonstrate the efficiency of the proposed preconditioned methods.
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Acknowledgements
The authors would like to thank the editor and two referees for their helpful comments and suggestions, which greatly improve the presentation. The first author also would like to thank Prof. Xuezhong Wang, Prof. Zhibao Li and Dr. Maolin Liang for providing their MATLAB codes and useful discussions on this topic. The first author was supported by the Opening Project of Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University (Grant No. 2018008) and the Natural Science Foundation of Guangdong Province (No. 2018A030313505). The second author is supported in part by National Natural Science Foundation of China (Grant Nos. 11671158, U1811464, 11771159). The third author was supported by University of Macau (Grant No. MYRG2017-00098-FST, MYRG2018-00047-FST) and the Macao Science and Technology Development Fund (0005/2019/A).
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Liu, D., Li, W. & Vong, SW. A new preconditioned SOR method for solving multi-linear systems with an \({\mathcal {M}}\)-tensor. Calcolo 57, 15 (2020). https://doi.org/10.1007/s10092-020-00364-8
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DOI: https://doi.org/10.1007/s10092-020-00364-8
Keywords
- Multi-linear system
- SOR method
- Preconditioned method
- Tensor splitting algorithm
- Stong \({\mathcal{M}}\)-tensor