Two-stage iterative methods for consistent Hermitian positive semidefinite systems Original Research Article

We study stationary and nonstationary two-stage iterative methods for the solution of consistent and singular linear systems Ax=b, where A is a Hermitian positive semidefinite matrix. When the outer splitting is P-regular and inner splitting is convergent, we prove the convergence of stationary two-stage iterative methods with inner iteration number q being a positive even number; conditions are given to ensure the convergence of stationary iterative methods for any positive inner iteration number q. Also, we present some theoretical results on the convergence of nonstationary two-stage methods. A comparison theorem is obtained for Hermitian positive semidefinite matrix and some applications to it are discussed. Moreover, we obtain a monotonicity result on the stationary two-stage iterative methods.