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We establish two types of block triangular preconditioners applied to the linear saddle point problems with the singular (1,1) block. These preconditioners are based on the results presented in the paper of Rees and Greif (2007). We study the spectral characteristics of the preconditioners and show that all eigenvalues of the preconditioned matrices are strongly clustered. The choice of the parameter is involved. Furthermore, we give the optimal parameter inpractical. Finally, numerical experiments are also reported for illustrating the efficiency of the presented preconditioners

New Block Triangular Preconditioners for Saddle Point Linear Systems with Highly Singular (1,1) Blocks