In this presentation, the progress of our development for parallel preconditioning method is reported. Our target is large-scale generalized eigenvalue problems derived from quantum physics applications, and we are going to solve the problems by preconditioned Krylov iterative methods on exa-scale systems. Generally, such coefficient matrices are very ill-conditioned, and we need special preconditioning methods in order to solve them by the iterative methods. In the present work, we proposed two types "regularization" methods, which include blocking and shifted diagonals of the coefficient matrices. We show the effects of these regularization methods on robust convergence of ICCG solvers for the target matrices. Moreover, effects of parallel block-multicoloring for the large-scale problems are also presented.