Abstract
We propose a new preconditioning strategy for the Krylov subspace method for solving a large sparse system Ax=b. The basic idea is to use an approximation to A^-1υ for K^-1υ: the benefit is substantial when the preconditioner K sufficiently approximates A. The preconditioning is performed by approximately solving Az=υ by some iterative method. Then different types of preconditioner can be applied at each iterative step. In the present paper, we combine the SOR method as a preconditioner and the GCR(m) method as a solver, and show that our preconditioning has lower iterative counts and shorter computation time than ILU(0).
