In this paper, we first introduce the situation of Incomplete Factorization(IF)preconditioners. Consequently, we reduce the block tridiagonal matrix with non-singular off-diagonal blocks into a model one that has only negative identity matrixfor its off-diagonals. Then we evaluate the block LU factors for the model with thehelp of M matrices. The analyses show that the evaluation is exact in some sense.For the matrices which have equal diagonal blocks and have only negative identityoff-diagonal blocks, the tendency of the factors are also focused on. Moreover,we construct a type of preconditioners with these evaluations and analyze thecondition number of the preconditioned matrices. For the model problem, we givethe evaluation and practical condition number, which shows that the evaluation isexact to some extent. At last, we implement four of these preconditioners and testthem for the model problem. The results show that our method is effective and theanalyses imply that they will be more efficient than others in parallel computing.
