Abstract
The Generalized Minimal RESidual (GMRES) method with variable preconditioning is an efficient method for solving a large sparse linear system Ax = b. It has been clarified by some numerical experiments that the Successive Over-Relaxation (SOR) method is more effective than Krylov subspace methods such as GMRES and ILU(0) preconditioned GMRES for performing variable preconditioning. However, SOR cannot be applied for performing variable preconditioning, when solving the linear system with zero diagonal entries. Therefore, we propose to make good use of a strategy proposed by Duff and Koster, namely, an algorithm for permuting large nonzero entries onto the diagonal in order to enable SOR to be used for performing variable preconditioning. By numerical experiments, we show the efficiency of the variable preconditioned GMRES using SOR when applying the algorithm for permuting large nonzero entries onto the diagonal.
