  We establish a new iterative method for solving a class of large and sparse
linear systems of equations with three-by-three block coefficient matrices
having saddle point structure. Convergence properties of the proposed method
are studied in details and its induced preconditioner is examined for
accelerating the convergence speed of generalized minimal residual (GMRES)
method. More precisely, we analyze the eigenvalue distribution of the
preconditioned matrix. Numerical experiments are reported to demonstrate the
effectiveness of the proposed preconditioner.
