New Preconditioners for Nonsymmetric Saddle Point Systems with Singular (1,1) Block

Abstract

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