A new generalized parameterized inexact Uzawa method for solving saddle point problems

作者：Dai Lifang; Liang Maolin^*; Fan Hongtao

来源：Applied Mathematics and Computation, 2015, 265: 414-430.

DOI：10.1016/j.amc.2015.05.021

• Saddle point problems
• Generalized parameterized inexact Uzawa method
• Convergence
• Semi-convergence
• Preconditioner

Recently, Bai, Parlett and Wang presented a class of parameterized inexact Uzawa (PIU) methods for solving saddle point problems (Bai et al., 2005). In this paper, we develop a new generalized PIU method for solving both nonsingular and singular saddle point problems. The necessary and sufficient conditions of the convergence (semi-convergence) for solving nonsingular (singular) saddle point problems are derived. Meanwhile, the characteristic of eigen-values of the iteration matrix corresponding to the above iteration method is discussed. We further show that the generalized PIU-type method proposed in this paper has a wider convergence (semi-convergence) region than some classical Uzawa methods, such as the inexact Uzawa method, the SOR-like method, the GSOR method and so on. Finally, numerical examples are given to illustrate the feasibility and efficiency of this method.

• 出版日期2015-8-15
• 单位天水师范学院; 兰州大学