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On parameterized generalized skew-Hermitian triangular splitting iteration method for singular and nonsingular saddle point problems

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  • Zhang, Guo-Feng
  • Liao, Li-Dan
  • Liang, Zhao-Zheng

Abstract

Recently, Krukier et al. (2014) and Dou et al. (2014) have studied the generalized skew-Hermitian triangular splitting (GSTS) iteration method for nonsingular and singular saddle point problems, respectively. In this paper, we further extend the GSTS method to a parameterized GSTS (PGSTS) method for solving non-Hermitian nonsingular and singular saddle point problems. By singular value decomposition technique, we derive conditions of the new iterative method for guaranteeing the convergence for non-Hermitian nonsingular saddle point problems and its semi-convergence for singular saddle point problems, respectively. In addition, the choice of the acceleration parameters in a practical manner is studied. Numerical experiments are provided, which further confirm our theoretical results and show the new method is feasible and effective for non-Hermitian nonsingular or singular saddle point problems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:254:y:2015:i:c:p:340-359
    DOI: 10.1016/j.amc.2014.12.120
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    Cited by:

    1. Li, Cheng-Liang & Ma, Chang-Feng, 2019. "An accelerated symmetric SOR-like method for augmented systems," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 408-417.
    2. 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.

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