The PSOR-like preconditioner for CGS method

The Krylov subspace methods include popular methods such as Conjugate Gradients(CG), BiConjugate Gradients(Bi-CG), Bi-CGstab, CGS and GMRES, etc. And there are the classical iterative method such as Jacobi, Gauss-Seidel and SOR. The preconditioner K approximates the coefficient matrix A under the assumption that Kv is solved more easily and faster than Av, where v is a vector which use in Krylov subspace algorithm. The Incomplete LU decomposition (ILU) and Incomplete Cholesky decomposition (IC) are more widely and frequently used method for designing the preconditioner. Recently, the methods, which compute the linear systemKz = v by a classical iterative method at each iteration of the Krylov subspace method, have proposed by many researchers. These methods are so-called Hybrid algorithm. In this paper, we propose the Hybrid algorithm which use the Preconditioned SOR-like method and a Krylov subspace methods.