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

2015 ◽  
Vol 254 ◽  
pp. 340-359 ◽  
Author(s):  
Guo-Feng Zhang ◽  
Li-Dan Liao ◽  
Zhao-Zheng Liang
Keyword(s):  
Saddle Point ◽  
Iteration Method ◽  
Saddle Point Problems ◽  
Splitting Iteration Method

A Fast Shift-Splitting Iteration Method for Nonsymmetric Saddle Point Problems

2017 ◽  
Vol 7 (1) ◽  
pp. 172-191 ◽  
Author(s):  
Quan-Yu Dou ◽  
Jun-Feng Yin ◽  
Ze-Yu Liao
Keyword(s):  
Saddle Point ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Saddle Point Problems ◽  
Splitting Technique ◽  
Splitting Iteration Method

AbstractBased on the shift-splitting technique and the idea of Hermitian and skew-Hermitian splitting, a fast shift-splitting iteration method is proposed for solving nonsingular and singular nonsymmetric saddle point problems in this paper. Convergence and semi-convergence of the proposed iteration method for nonsingular and singular cases are carefully studied, respectively. Numerical experiments are implemented to demonstrate the feasibility and effectiveness of the proposed method.

A New Uzawa-Type Iteration Method for Non-Hermitian Saddle-Point Problems

2017 ◽  
Vol 7 (1) ◽  
pp. 211-226
Author(s):  
Yan Dou ◽  
Ai-Li Yang ◽  
Yu-Jiang Wu
Keyword(s):  
Saddle Point ◽  
Iteration Method ◽  
Spectral Properties ◽  
Numerical Results ◽  
Saddle Point Problems ◽  
Convergence Properties ◽  
Saddle Point Matrix

AbstractBased on a preconditioned shift-splitting of the (1,1)-block of non-Hermitian saddle-point matrix and the Uzawa iteration method, we establish a new Uzawa-type iteration method. The convergence properties of this iteration method are analyzed. In addition, based on this iteration method, a preconditioner is proposed. The spectral properties of the preconditioned saddle-point matrix are also analyzed. Numerical results are presented to verify the robustness and the efficiency of the new iteration method and the preconditioner.

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