A class of efficient parameterized shift-splitting preconditioners for block two-by-two linear systems

Abstract

Based on the effective constructing an equivalent block two-by-two linear systems, we establish a class of efficient parameterized shift-splitting (EPS) preconditioners for solving block two-by-two linear systems. Theoretical analysis shows that the EPS iteration method is unconditionally convergent, and then we study the spectral properties of the corresponding preconditioned matrix. By removing one of the shift term of the EPS preconditioners, two classes of local EPS preconditioners are presented and the eigenvalues distribution of the preconditioned matrices are also studied. Numerical experiments are provided to demonstrate the feasibility and effectiveness of the proposed preconditioners.