A new relaxed PSS preconditioner for nonsymmetric saddle point problems

A new relaxed PSS-like iteration scheme for the nonsymmetric saddle point problem is proposed. As a stationary iterative method, the new variant is proved to converge unconditionally. When used for preconditioning, the preconditioner differs from the coefficient matrix only in the upper-right components. The theoretical analysis shows that the preconditioned matrix has a well-clustered eigenvalues around (1, 0) with a reasonable choice of the relaxation parameter. This sound property is desirable in that the related Krylov subspace method can converge much faster, which is validated by numerical examples.