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A new preconditioner for a class of \(2\times 2\) block linear systems

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Abstract

In this paper, a new preconditioner for a class of \(2\times 2\) block linear systems is proposed. The proposed new preconditioner is a better approximation to the original coefficient matrix than the previous ones. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are discussed. Finally, two numerical examples are provided to show the effectiveness of the proposed preconditioner.

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Acknowledgements

I would like to thank Professor Ken Hayami of the National Institute of Informatics, Tokyo, Japan for his hospitality during my visit at the National Institute of Informatics. I also would like to thank Professor Yang Cao (Nantong University) for his invaluable suggestion. Many thanks to the Editor and the anonymous referees for their constructive and helpful comments on the revision of this article.

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  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, China

    Shu-Xin Miao

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  1. Shu-Xin Miao
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Correspondence to Shu-Xin Miao.

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This work was supported by the National Natural Science Foundation of China (No. 11861059).

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Miao, SX. A new preconditioner for a class of \(2\times 2\) block linear systems. Japan J. Indust. Appl. Math. 37, 913–928 (2020). https://doi.org/10.1007/s13160-020-00425-z

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  • DOI: https://doi.org/10.1007/s13160-020-00425-z

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