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A generalized shift-splitting preconditioner for singular saddle point problems

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  • Chen, Cai-Rong
  • Ma, Chang-Feng

Abstract

Recently, some authors (Cao et al., 2014; Chen and Ma, 2015; Salkuyeh et al., 2014) discussed the (generalized) shift-splitting preconditioner for nonsingular saddle point problems. In this paper, we further study the generalized shift-splitting preconditioner for solving singular saddle point problems with symmetric positive definite (1, 1)-block. Theoretical analysis shows that the generalized shift-splitting iteration method is unconditionally semi-convergent. Numerical experiments are given to illustrate the efficiency of the proposed preconditioner with appropriate parameters.

Suggested Citation

  • Chen, Cai-Rong & Ma, Chang-Feng, 2015. "A generalized shift-splitting preconditioner for singular saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 947-955.
    • Handle: RePEc:eee:apmaco:v:269:y:2015:i:c:p:947-955
    DOI: 10.1016/j.amc.2015.08.020
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    References listed on IDEAS

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    1. Yang, Ai-Li & Li, Xu & Wu, Yu-Jiang, 2015. "On semi-convergence of the Uzawa–HSS method for singular saddle-point problems," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 88-98.
    2. Huang, Na & Ma, Changfeng, 2015. "The BGS–Uzawa and BJ–Uzawa iterative methods for solving the saddle point problem," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 94-108.
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    Cited by:

    1. Li, Zhizhi & Chu, Risheng & Zhang, Huai, 2019. "Accelerating the shift-splitting iteration algorithm," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 421-429.
    2. Ke, Yi-Fen & Ma, Chang-Feng, 2017. "The dimensional splitting iteration methods for solving saddle point problems arising from time-harmonic eddy current models," Applied Mathematics and Computation, Elsevier, vol. 303(C), pages 146-164.
    3. Li, Chengliang & Ma, Changfeng & Xu, Xiaofang, 2020. "A class of efficient parameterized shift-splitting preconditioners for block two-by-two linear systems," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    4. Ling, Si-Tao & Liu, Qing-Bing, 2017. "New local generalized shift-splitting preconditioners for saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 302(C), pages 58-67.
    5. Huang, Zheng-Ge & Wang, Li-Gong & Xu, Zhong & Cui, Jing-Jing, 2017. "The generalized modified shift-splitting preconditioners for nonsymmetric saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 95-118.
    6. Huang, Na & Ma, Chang-Feng & Xie, Ya-Jun, 2015. "An inexact relaxed DPSS preconditioner for saddle point problem," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 431-447.

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