A Proposed, Performance Estimation of GMRES(k) Method with Stationary Type Preconditioners

Abstract

  The restarted GMRES(k) method is an effective means for solving linear systems of equations where the coefficient matrix is nonsymmetric. The incomplete LU factorization without extra fill-ins is a widely used preconditioning. Sometimes this preconditioning works well. However, sometimes it does not work well at all. We propose an efficient and robust preconditioning technique based on iteration matrices of stationary methods, e.g., Gauss-Seidel and SOR methods. Through numerical experiments, we verify the effectiveness of the proposed preconditioning.