A shift-splitting preconditioner for a class of block two-by-two linear systems

In this paper, we construct a shift-splitting preconditioner for a class of block two-by-two linear systems. The proposed preconditioner is extracted from a stationary iterative method which is unconditionally convergent. Moreover, the eigenvalue distribution of the corresponding preconditioned matrix is studied. Numerical experiments are presented to show that our new preconditioner can be quite competitive when used to precondition Krylov subspace iterative methods such as GMRES.