Cholesky factorization of the augmented system in interior point method for linear programming

In the normal equations approach in which the ordering and factorization phases are separated, the factorization in the augmented system approach is computed dynamically. This means that in the augmented system the numerical factorization should be performed to obtain the non-zero structure of Cholesky factor L. This causes much time to set up the non-zero structure of Cholesky L. So, we present a method which can separate the ordering and numerical factorization in the augmented system. Experimental results show that the proposed method reduced the time for obtaining the non-zero structure of Cholesky factor L.