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On semi-convergence of the Uzawa–HSS method for singular saddle-point problems

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  • Yang, Ai-Li
  • Li, Xu
  • Wu, Yu-Jiang

Abstract

Based on the Hermitian and skew-Hermitian splitting (HSS) iteration scheme, an efficient Uzawa–HSS iteration method has been proposed to solve the nonsingular saddle-point problems. In this paper, we discuss the feasibility of the Uzawa–HSS method used for solving singular saddle-point problems. The semi-convergence properties of the Uzawa–HSS iteration method are carefully analyzed, which show that the iterative sequence generated by the Uzawa–HSS method converges to a solution of the singular saddle-point problem if the iteration parameters satisfy suitable restrictions. Numerical results verify the robustness and efficiency of the Uzawa–HSS method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:252:y:2015:i:c:p:88-98
    DOI: 10.1016/j.amc.2014.11.100
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    Cited by:

    1. Cao, Yang & Yi, Shi-Chao, 2016. "A class of Uzawa-PSS iteration methods for nonsingular and singular non-Hermitian saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 41-49.
    2. 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.
    3. Dai, Lifang & Liang, Maolin & Fan, Hongtao, 2015. "A new generalized parameterized inexact Uzawa method for solving saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 414-430.
    4. Miao, Shu-Xin, 2017. "A new Uzawa-type method for saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 300(C), pages 95-102.
    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.

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