Abstract: Using the method of high order approximate LU dicomposition, the preconditioning matrices of high order ICCG are given and the ‖R_p‖_∞ is also estimated when P=3 and 4. The upper bounds of Cond (L_PU_P)^-1A for P=3 and 4 are obtained respectively. For different mesh sizes, the computed results of Cond (L_PU_P)^-1A are also compared with the theoretical upper bound.

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