We investigate the solution of large linear systems of saddle point type with singular (1, 1) block by preconditioned iterative\r\nmethods and consider two parameterized block triangular preconditioners used with Krylov subspace methods which have the\r\nattractive property of improved eigenvalue clustering with increased ill-conditioning of the (1, 1) block of the saddle point matrix,\r\nincluding the choice of the parameter. Meanwhile, we analyze the spectral characteristics of two preconditioners and give the\r\noptimal parameter in practice. Numerical experiments that validate the analysis are presented.
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