Abstract
In recent years, the method of solving the multi-linear systems has received much attention. In this paper, the multi-linear systems with more general \({\mathcal {Z}}\)-tensors which have wider applications than \({\mathcal {M}}\)-tensors are studied. Two different SOR-type splitting methods and a general preconditioner that can include some known preconditioners are provided. In addition, some comparisons of spectral radius between the preconditioned iterative tensors and the original one are given. Numerical examples are given to illustrate our theoretical results and demonstrate the efficiency of the proposed preconditioned methods.
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Acknowledgements
The authors are grateful to the handling Associate Editor and anonymous referees for useful comments and suggestions that contributed to improving the quality of the manuscript. This research is supported in part by National Natural Science Foundations of China(No.11601134,11571095), Foundation of Henan Educational Committee(No.21A110013), Foundation of Henan Normal University (No.2021PL03), Natural Science Foundations of Henan (No.202300410236), 2020 Scientific Research Project for Postgraduates of Henan Normal University (No.YL202021).
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Cui, LB., Fan, YD. & Zheng, YT. A general preconditioner accelerated SOR-type iterative method for multi-linear systems with \({\mathcal {Z}}\)-tensors. Comp. Appl. Math. 41, 26 (2022). https://doi.org/10.1007/s40314-021-01712-2
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DOI: https://doi.org/10.1007/s40314-021-01712-2