Abstract
As preconditioners for complex symmetric systems of linear equations, incomplete Cholesky decomposition and complex shifted incomplete Cholesky decomposition are well-known. These preconditioners have two parameters, threshold value and shift parameter. It is difficult to choose effective parameters for these preconditioners. In this paper, we evaluate preconditioning matrices by using Precise Remainder Index (PRI) in order to choose effective parameters. We investigate the relationship between the number of iterations in Krylov subspace iterative method and PRI by numerical experiments.
