Variants of the Uzawa method for three-order block saddle point problem

In this paper, we first propose three kinds of variants of the Uzawa method for solving three-order block saddle point problem and study the convergence conditions of the proposed methods. Second, we obtain the approximate optimal relaxation factors of the three proposed Uzawa type methods by using variable control method. Finally, the experimental results show that our proposed Uzawa type methods for solving three-order block saddle point problem have less workload per iteration step than the corresponding Uzawa type methods for solving standard saddle point problem, which explains that our proposed methods are feasible and efficient.