Improved Relaxed Positive-Definite and Skew-Hermitian Splitting Preconditioners for Saddle Point Problems (Journal of Computational Mathematics, 2018)
We establish a class of improved relaxed positive-definite and skew-Hermitian splitting(IRPSS) preconditioners for saddle point problems. These preconditioners are easier tobe implemented than the relaxed positive-definite and skew-Hermitian splitting (RPSS)preconditioner at each step for solving the saddle point problem. We study spectral propertiesand the minimal polynomial of the IRPSS preconditioned saddle point matrix. Atheoretical optimal IRPSS preconditioner is also obtained. Numerical results show thatour proposed IRPSS preconditioners are superior to the existing ones in accelerating theconvergence rate of the GMRES method for solving saddle point problems.
Keywords: Saddle point problems; Preconditioning; RPSS preconditioner; Eigenvalues; Krylov subspace method.