非Hermite正定线性代数方程组的两参数预处理NSS方法(英文)

Two-parameter preconditioned NSS method for non-Hermitian and positive definite linear systems

对大型稀疏的非Hermite正定线性代数方程组,运用正规和反Hermite分裂(normal and skew-Hermitian splitting,NSS)迭代技巧,提出了一种两参数预处理NSS迭代法,它实际上是预处理NSS方法的推广.理论分析表明,新方法收敛于线性方程组的唯一解.进一步地,推导了出现于新方法中的两个参数的最优选取,计算了对应的迭代谱的上界的最小值.新方法的实际实施中,还将不完全LU分解和增量未知元选做了两类预处理子.数值结果对所给方法的收敛性理论和有效性予以了证实.

By using the normal and skew-Hermitian splitting （NSS） iteration technique for large sparse non-Hermitian and positive definite linear systems, a two-parameter preconditioned NSS iteration, which gives the actually generalized form of the preconditioned NSS method is proposed. Theoretical analysis shows that the new iterative method converges to the unique solution of the linear system. Moreover, the optimal choice of two parameters involved in the new method and the corresponding minimum value for the upper bound of the iterative spectrum are derived and computed. For the actual implementation of this method, the in- complete LU （ILU） decomposition and the incremental unknowns （IUs） are chosen as two types of the preconditioners. Numerical results confirm the analysis of the convergence theory and the effectiveness of the proposed method.