Comparison of some Preconditioned Krylov Methods for Solving Sparse Non-symmetric Linear Systems of Equations

Large sparse non-symmetric linear systems of equations often occur in many scientific and engineering applications. In this paper, we present a comparative study of some preconditioned Krylov iterative methods, namely CGS, Bi-CGSTAB, TFQMR and GMRES for solving such systems. To demonstrate their efficiency, we test and compare the numerical implementations of these methods on five numerical examples. The preconditioners considered here are incomplete LU-decomposition (ILU), Symmetric Successive Over Relaxation (SSOR), and Alternating Direction Implicit (ADI). The ILU preconditioner is shown to be extremely effective in achieving optimal convergence rates for the class of problems considered here. Finally, our results show that the GMRES is the best among the considered iterative methods.