A two-parameter shift-splitting preconditioner for saddle point problems

Abstract

For saddle point problems, a two-parameter shift-splitting (TPSS) preconditioner is proposed. Estimated lower and upper bounds of the real eigenvalues and the real and imaginary parts of the non-real eigenvalues of the TPSS preconditioned matrix are obtained, respectively. As special cases, bounds obtained are tighter than the ones for the GSS, PGSS, IGSS and NESS preconditioners, respectively. Meanwhile, the corresponding TPSS iteration method is constructed and the convergence analysis is studied. Numerical experiments for two frequently used problems are given to illustrate the great robustness of the TPSS preconditioner.