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A class of Uzawa-PSS iteration methods for nonsingular and singular non-Hermitian saddle point problems

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  • Cao, Yang
  • Yi, Shi-Chao

Abstract

In this paper, based on the positive definite and skew-Hermitian splitting iteration scheme and the Uzawa iteration method, we propose a class of Uzawa-PSS iteration methods for solving nonsingular and singular non-Hermitian saddle point problems with (1,1) block of the saddle point matrix being non-Hermitian positive definite. We derive conditions of the new iteration method for guaranteeing the convergence for nonsingular saddle point problems and its semi-convergence for singular saddle point problems, respectively. Numerical experiments of a model Navier–Stokes problem are presented to illustrate the effectiveness of the Uzawa-PSS iteration method. Numerical results show that the new method is much efficient than the Uzawa-HSS iteration method for solving both the nonsingular saddle point problems Yang and Wu, (2014) [28] and the singular saddle point problems Yang, Li and Wu, (2015) [30].

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:275:y:2016:i:c:p:41-49
    DOI: 10.1016/j.amc.2015.11.049
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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. Zhang, Guo-Feng & Liao, Li-Dan & Liang, Zhao-Zheng, 2015. "On parameterized generalized skew-Hermitian triangular splitting iteration method for singular and nonsingular saddle point problems," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 340-359.
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