块三对角阵分解因子的估值与应用

1.引 言 许多物理应用问题归结为求微分方程数值解,而这可以通过离散化为求解稀疏线性方程组,所以稀疏线性方程组求解的有效性在很大程度上决定了原问题求解算法的有效性.直接

EVALUATING THE FACTORS OF BLOCK TRIDIAGONAL MATRIX AND ITS APPLICATION

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 matrix for its off-diagonals. Then we evaluate the block LU factors for the model with the help 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 identity off-diagonal blocks, the tendency of the factors are also focused on. Moreover, we construct a type of preconditioners with these evaluations and analyze the condition number of the preconditioned matrices. For the model problem, we give the evaluation and practical condition number, which shows that the evaluation is exact to some extent. At last, we implement four of these preconditioners and test them for the model problem. The results show that our method is effective and the analyses imply that they will be more efficient than others in parallel computing.