Abstract: Using a model problem and the method of high order approximate LU dicomposition, the preconditioning matrices of ICCG are given and the ‖R_p‖_∞ is also estimated. Based on these results, the upper bound of condition numbers of ICCG (s,t) when (s,t)=(1,1),(1,2) and (1,3) are given respectively. For different mesh sizes, the computed results are compared with the theoretical results of this paper.

Key words: ICCG method, high order approximate LU decomposition, error matrix, condition number