An optimized computer implementation of incomplete Cholesky factorization

Abstract

Preconditioning techniques based on incomplete Cholesky factorization are very efficient in increasing the convergence rates of basic iterative methods. Complicated addressings and high demands for auxiliary storage, or increased factorization time, have reduced their appeal as general purpose preconditioners. In this study an elegant computational implementation is presented which succeeds in reducing both computing storage and factorization time. The proposed implementation is applied to two incomplete factorization schemes. The first is based on the rejection of certain terms according to their magnitude, while the second is based on a rejection criterion relative to the position of the zero terms of the coefficient matrix. Numerical results demonstrate the superiority of the proposed preconditioners over other types of preconditioning matrices, particularly for ill-conditioned problems. They also show their efficiency for large-scale problems in terms of computer storage and CPU time, over a direct solution method using the skyline storage scheme.