A modified relaxed splitting preconditioner for generalized saddle point problems from the incompressible Navier–Stokes equations

Based on a new matrix splitting of the original coefficient matrix, a modified relaxed splitting (MRS) preconditioner for generalized saddle point problems from the incompressible Navier–Stokes equations is considered. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are studied. The proposed preconditioner is closer to the original matrix than the generalized relaxed splitting (GRS) preconditioner in the sense of certain norm, which straightforwardly results in a MRS iteration method. Finally, numerical results are given to demonstrate the theoretical analysis. The results show that this novel preconditioner is competitive with and more effective than some of the best existing preconditioners.