非埃尔米特正定线性系统的预条件NSS方法

基于大型稀疏非埃尔米特正定线性系统的正规/反对称分裂(NSS)方法,提出了预条件正规/反对称分裂(PNSS)迭代方法,并讨论了这些方法的变形,例如,不精确的预条件正规/反对称分裂(IPNSS)方法。理论分析表明,在一定条件下,新的迭代格式是收敛的。给出了迭代格式中参数和迭代矩阵谱半径的最小上界的计算方法。在数值实验中,选取增量未知元(IUs)和对称逐次超松弛(SSOR)两种预处理矩阵。数值结果证明了收敛定理的正确性和方法的有效性。

Preconditioned NSS methods for non-Hermitian and positive definite linear systems

Based on the normal/skew-Hermitian splitting(NSS) iteration technique for large sparse non-Hermitian and positive definite linear systems,preconditioned normal/skew-Hermitian splitting(PNSS) methods and investigation of their variants are proposed,e.g.,the inexact preconditioned normal/skew-Hermitian splitting(IPNSS) methods.Theoretical analysis shows that the PNSS methods are convergent under some conditions.Also,the computational methods of the optimal choice of the parameter are presented as involved in our iterative schemes and the corresponding minimum values for the upper bound of the iterative spectrums.In the numerical test,we choose incremental unknowns(IUs) and symmetric successive overrelaxation(SSOR) as two types of our precondioners.Numerical results confirm the correctness of the convergence theory and the effectiveness of the proposed methods.