The BGS-Uzawa and BJ-Uzawa iterative methods for solving the saddle point problem

In this paper, we propose two new iterative methods for solving the nonsingular saddle point problem based on partitioning the coefficient matrix. One is combining the block Gauss-Seidel iterative method with the Uzawa iterative method, and the other one is combining the block Jacobi iterative method with the Uzawa iterative method. Then we study the convergence of the two novel methods under suitable restrictions on the iteration parameters, respectively. Numerical experiments are also presented to illustrate the behavior of the considered algorithms.