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An equidistant parameterized Gauss–Seidel iteration method for a class of block two-by-two linear systems

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Abstract

In this work, an equidistant parameterized Gauss–Seidel (EPGS) iteration method based on a scale-splitting formulation of matrix is proposed for solving a class of block two-by-two real linear systems. Then, we investigate the convergence properties of this method and derive the optimal value of a relaxation parameter as well as the corresponding convergence factor. Furthermore, the spectral properties of EPGS-preconditioner are studied when the EPGS splitting matrix serves as a preconditioner to improve Krylov subspace methods. Finally, some numerical experiments are performed and discussed to demonstrate the performance of our method, and numerical results show that this novel method outperforms than classical iteration methods including PMHSS, E-HS, and GSOR.

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Acknowledgements

This work is supported by “GDAS’ Project of Science and Technology Development NO: 2018GDASCX-0804.” The authors wish to thank Prof. Dr. Lei Zhang for valuable suggestions which improved the quality of the paper. Thanks to the anonymous referees for their constructive suggestions and helpful comments, which greatly improved the original manuscript of this paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    Xi-An Li

  2. Guangdong Institute of Aeronautics and Astronautics Equipment & Technology, Zhuhai, 519000, People’s Republic of China

    Jian Lu

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  1. Xi-An Li
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  2. Jian Lu
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Correspondence to Xi-An Li or Jian Lu.

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Communicated by Zhong-Zhi Bai.

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Li, XA., Lu, J. An equidistant parameterized Gauss–Seidel iteration method for a class of block two-by-two linear systems. Comp. Appl. Math. 39, 292 (2020). https://doi.org/10.1007/s40314-020-01341-1

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  • DOI: https://doi.org/10.1007/s40314-020-01341-1

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