Abstract
By combining the preconditioner \(I+S_{\varvec{\alpha }}\) by Li et al. (Appl Numer Math 134:105–121, 2018) and some elements of the last row of the majorization matrix associated with the coefficient tensor, we propose a new preconditioner and present the corresponding preconditioned Gauss–Seidel method for solving multi-linear systems with \(\mathcal {M}\)-tensors. Theoretically, we give the convergence and comparison theorems of the proposed preconditioned Gauss–Seidel method. Numerical examples are given to show our theoretical results and the efficiency of the proposed preconditioner.
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Acknowledgements
This research was partially supported by the National Natural Science Foundation of China (No.61967014), the Foundation for Distinguished Young Scholars of Gansu Province (No. 20JR5RA540).
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Xie, K., Miao, SX. A new preconditioner for Gauss–Seidel method for solving multi-linear systems. Japan J. Indust. Appl. Math. 40, 1159–1173 (2023). https://doi.org/10.1007/s13160-023-00573-y
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DOI: https://doi.org/10.1007/s13160-023-00573-y