This article introduces an iterative method for solving nonsingular non-Hermitian positive semidefinite systems of linear equations. To construct the iteration process, the coefficient matrix is split into two non-Hermitian positive semidefinite matrices along with an arbitrary Hermitian positive definite shift matrix. Several conditions are established to guarantee the convergence of method and suggestions are provided for selecting the matrices involved in the desired splitting. We explore selection process of the shift matrix and determine the optimal parameter in a specific scenario. The proposed method aims to generalize previous approaches and improve the conditions for convergence theorems. In addition, we examine two special cases of this method and compare the induced preconditioners with some state-of-art preconditioners. Numerical examples are given to demonstrate effectiveness of the presented preconditioners.

翻译：本文介绍了一种用于求解非奇异非厄米正定线性方程组的迭代方法。为构建迭代过程，系数矩阵被分解为两个非厄米正定矩阵，并引入一个任意的厄米正定平移矩阵。我们建立了若干条件以保证方法的收敛性，并为期望分裂中所涉及的矩阵选择提供了建议。我们探讨了平移矩阵的选取过程，并在特定场景下确定了最优参数。所提出的方法旨在推广先前方法并改进收敛定理的条件。此外，我们研究了该方法的两种特殊情况，并将导出的预条件子与若干先进预条件子进行了比较。数值算例验证了所提出预条件子的有效性。