A new Uzawa-type method for saddle point problems

Based on the Hermitian and skew-Hermitian splitting of the non-Hermitian positive definite (1, 1)-block of the saddle point matrix, a new Uzawa-type iteration method is proposed for solving a class of saddle point problems in this paper. The proposed method can be applied not only to the nonsingular saddle point problems but also to the singular ones. The convergence properties for the nonsingular saddle point problems and the semi-convergence properties for the singular ones of the proposed method are carefully discussed under suitable restrictions. Numerical results verify the effectiveness and robustness of the proposed method.