We consider the solution of linear system with a block-structured matrix of saddle point type. The solution technique is based on the idea of the classical
alternating-direction implicit iterative method where symmetric-antisymmetric
splitting of the coefficient matrix is used. To find an optimal parameter for
solving the system with a symmetric matrix, the polynomial filters are considered. The CGW method is used for systems with skew-symmetric matrix. The numerical tests compare the results obtained by using alternating iteration and GMRES and point out advantages of alternative iterations for larger systems.