Abstract: Using the method of the element order in matrices, high order approximate LU decompositions are used as the preconditioners for the computation of different experiments. High order approximate inverses are also adopted for the approximate block LU decomposition in the computation of the block-PCG for same experiments. The results show that the point-PCG of order P has a higher convergence rate than the block-PCG of order P when P=2.3,…,6. The total computational cost of the point-PCG is less than the block-PCG of Ihe same order. This illustates that the point-PCG of the P-order approximate LU decomposition is more efficient than the block-PCG of the P-order approximate inverse when the order P varies in the scope considered.