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| 鞍点问题的广义位移分裂预条件子 | |
| 引用本文： | 曹阳,陶怀仁,蒋美群.鞍点问题的广义位移分裂预条件子[J].计算数学,2014,36(1):16-26. |
| 作者姓名： | 曹阳 陶怀仁 蒋美群 |
| 作者单位： | 1. 南通大学交通学院, 江苏南通 226019; 2. 苏州大学数学科学学院, 江苏苏州 215006 |
| 基金项目： | 国家自然科学基金项目（11301290）资助. |
| 摘 要： | 对于大型稀疏非Hermitian正定线性方程组,Bai等人提出了一种位移分裂预条件子(J.Comput.Math.,24(2006)539-552).本文将这种思想用到鞍点问题上并提出了一种广义位移分裂(Generalized Shift Splitting,GSS)预条件子,同时证明了该预条件子所对应分裂迭代法的无条件收敛性.最后用数值算例验证了新预条件子的有效性. |
| 关 键 词： | 鞍点问题 广义位移分裂迭代法 收敛性 预处理 |
| 收稿时间： | 2013-03-01; |
GENERALIZED SHIFT SPLITTING PRECONDITIONERS FOR SADDLE POINT PROBLEMS |
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| Cao Yang,Tao Huairen,Jiang Meiqun.GENERALIZED SHIFT SPLITTING PRECONDITIONERS FOR SADDLE POINT PROBLEMS[J].Mathematica Numerica Sinica,2014,36(1):16-26. | |
| Authors: | Cao Yang Tao Huairen Jiang Meiqun |
| Institution: | 1. School of Transportation, Nantong University, Nantong 226019, Jiangsu, China; 2. School of Mathematics Sciences, Soochow University, Suzhou 215006, Jiangsu, China |
| Abstract: | For large and sparse non-Hermitian positive definite linear systems, Bai et al. proposed a shift splitting preconditioner (J. Comput. Math., 24 (2006) 539-552). In this paper, we extend this idea to study saddle point problems and present a generalized shift splitting preconditioner. The unconditional convergent property of the corresponding iterative method is proved. Finally, some numerical experiments are illustrated to show the efficiency of the new preconditioners. |
| Keywords: | saddle point problems generalized shift splitting iteration method convergence preconditioning |
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