  In this paper, the generalized shift-splitting preconditioner is implemented
for saddle point problems with symmetric positive definite (1,1)-block and
symmetric positive semidefinite (2,2)-block. The proposed preconditioner is
extracted form a stationary iterative method which is unconditionally
convergent. Moreover, a relaxed version of the proposed preconditioner is
presented and some properties of the eigenvalues distribution of the
corresponding preconditioned matrix are studied. Finally, some numerical
experiments on test problems arisen from finite element discretization of the
Stokes problem are given to show the effectiveness of the preconditioners.
