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On the improvement of shift-splitting preconditioners for double saddle point problems

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Abstract

The shift-splitting preconditioner is investigated and improved within relaxation and preconditioning techniques to solve a special double saddle point problem in block three-by-three form. The proposed preconditioner can also be viewed as a generalization of the regularized preconditioner for standard saddle point problem. For economical implementation purpose, a further modification of the proposed preconditioner is also developed by utilizing an inexact block factorization technique to avoid the high cost of storage and computing requirements for solving the arising augmentation type linear subsystems. Moreover, spectral properties of the preconditioned matrices are analyzed in detail and valid lower and upper bounds are obtained to restrict the area confining the real and non-real eigenvalues, respectively. Numerical experiments are performed to assess the efficiency of the new preconditioners within Krylov subspace acceleration.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People’s Republic of China

    Zhao-Zheng Liang

  2. School of Mathematics and Statistics, Hexi University, Zhangye, 734000, People’s Republic of China

    Mu-Zheng Zhu

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  1. Zhao-Zheng Liang
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  2. Mu-Zheng Zhu
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Z-ZL: conceptualization, methodology, software, writing-reviewing & editing. M-ZZ: validation, reviewing & editing.

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Correspondence to Zhao-Zheng Liang.

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This work was supported by the National Natural Science Foundation of China (Nos. 11801242), the Fundamental Research Funds for the Central Universities (No. lzujbky-2022-05) and the Natural Science Foundation of Gansu Province (Nos. 23JRRA1104, 21JR7RA553).

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Liang, ZZ., Zhu, MZ. On the improvement of shift-splitting preconditioners for double saddle point problems. J. Appl. Math. Comput. 70, 1339–1363 (2024). https://doi.org/10.1007/s12190-024-02003-9

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  • DOI: https://doi.org/10.1007/s12190-024-02003-9

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