Minimum residual shift-splitting iteration method for non-Hermitian positive definite and positive semidefinite linear systems

Abstract

By applying the minimum residual technique to the shift-splitting (SS) iteration scheme, we introduce a non-stationary iteration method named minimum residual SS (MRSS) iteration method to solve non-Hermitian positive definite and positive semidefinite systems of linear equations. Theoretical analyses show that the MRSS iteration method is unconditionally convergent for both of the two kinds of systems of linear equations. Numerical examples are employed to verify the feasibility and effectiveness of the MRSS iteration method.