Some conditions for existence and stability of relaxed incomplete LU factorizations Original Research Article

We present a condition for the existence of the relaxed incomplete LU factorization (RILU) (Axelsson and Lindskog, 1986), and based on the analytical results of Elman (1986, 1989), we show the conditions for the stability of the computations involving the triangular factors in the RILU preconditioning operation during the preconditioned iterative process. These conditions are related to the relaxation parameter ω and the focus is mainly on RILU(1,ω). Our analysis consists of an analytical and numerical study of a class of pentadiagonal matrices. The numerical experiments show that these conditions play an important role in obtaining an efficient RILU preconditioner, and show that the relaxation parameter ω could also play an important role in obtaining an efficient RILU preconditioner.