A class of accelerated Uzawa algorithms for saddle point problems

作者：Zheng, Qingqing; Ma, Changfeng^*

来源：Applied Mathematics and Computation, 2014, 247: 244-254.

DOI：10.1016/j.amc.2014.08.104

• Saddle point problem
• The Uzawa method
• Extrapolation technique
• The AU method
• Convergence analysis

In this paper, we establish a class of accelerated Uzawa (AU) algorithms for solving the large sparse nonsingular saddle point problems by making use of the extrapolation technique. This extrapolation technique is based on the eigenvalues of the iterative matrix. These AU algorithms involve two iteration parameters whose special choices can cover the known classical Uzawa method, as well as yield new ones. Firstly, the accelerated model for the Uzawa algorithm is established and the detail algorithm description of AU method is presented. Then the convergence analyse of the AU method is given. Moreover, theoretical analyses show that the AU algorithm converges faster than some Uzawa-type methods (the Uzawa method is also included in) when the eigenvalues of the iterative matrix and the parameter tau satisfy some conditions. Numerical experiments on a few model problems are presented to illustrate the theoretical results and examine the numerical effectiveness of the AU method.

• 出版日期2014-11-15
• 单位福建师范大学