In this paper, to find the numerical solution of the linear systems with the non-Hermitian positive definite matrix, a preconditioned two-sweep shift splitting (PTSS) iteration method is introduced and its convergent conditions are discussed. When the PTSS method is used as a preconditioner, the eigenvalue distribution of the corresponding preconditioned matrix is given. Numerical experiments are reported to the efficiency of the PTSS method and the PTSS preconditioner.

中文翻译：

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非厄尔米特正定线性系统的预处理二次扫描移位分裂方法

在本文中，为了找到具有非厄米正定矩阵的线性系统的数值解，引入了预处理的二次扫描移位分裂（PTSS）迭代方法并讨论了其收敛条件。当使用PTSS方法作为预条件子时，给出相应预条件矩阵的特征值分布。数值实验报告了 PTSS 方法和 PTSS 预处理器的效率。