A relaxed splitting preconditioner for generalized saddle point problems

In this paper, a new relaxed splitting preconditioner is proposed for the generalized saddle point problems. The proposed preconditioner is based on a new matrix splitting of the coefficient matrix and is easier to be implemented than the dimensional splitting preconditioner. Eigenvalue distribution of the preconditioned matrix is analyzed. An upper bound of the degree of the minimal polynomial of the preconditioned matrix is discussed. Finally, some numerical experiments are illustrated to show the efficiency of the new preconditioner.