MINRES Seed Projection Methods for Solving Symmetric Linear Systems with Multiple Right-Hand Sides

We consider the MINRES seed projection method for solving multiple right-hand side linear systems AX=B, where A∈Rn×n is a nonsingular symmetric matrix, B∈Rn×p. In general, GMRES seed projection method is one of the effective methods for solving multiple right-hand side linear systems. However, when the coefficient matrix is symmetric, the efficiency of this method would be weak. MINRES seed projection method for solving symmetric systems with multiple right-hand sides is proposed in this paper, and the residual estimation is analyzed. The numerical examples show the efficiency of this method.