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A preconditioned tensor splitting iteration method and associated global correction technique for solving multilinear systems

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Abstract

In this work, we propose a preconditioned tensor splitting iteration method for solving the multilinear system with Einstein product and give the corresponding theoretical analysis. Then we give a global correction method and theoretically prove that the proposed global correction method accelerates the convergence of the existing algorithm. These studies give some new accelerated iterative techniques which are not appeared in the previously published works. Some numerical results are disclosed to experimentally illustrate the effectiveness of the preconditioned method and the global correction technique.

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Acknowledgements

We are grateful to the anonymous referees for their valuable suggestions and constructive comments which have considerably improved this paper. We would like to thank the supports of the National Natural Science Foundation of China (12001211, 12071159, 12171168) and Natural Science Foundation of Fujian Province, China (2022J01194).

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  1. School of Mathematics and Statistics, Fujian Normal University, Fuzhou, 350117, People’s Republic of China

    Baohua Huang

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  1. Baohua Huang
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The work is supported by National Natural Science Foundation of China (12001211, 12071159, 12171168) and Natural Science Foundation of Fujian Province, China (2022J01194)

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Huang, B. A preconditioned tensor splitting iteration method and associated global correction technique for solving multilinear systems. Calcolo 60, 4 (2023). https://doi.org/10.1007/s10092-022-00499-w

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