In this paper we make two new lopsided methods (LTSCSP1 and LTSCSP2) based on the two-scale-splitting (TSCSP) method and show that the convergence speed of TSCSP iteration method can be increased under some conditions without adding any additional parameter. The convergence analysis of the new methods in detail is given. Then we will obtain the quasi-optimal parameter to minimize the spectral radius of iteration matrix for the new methods. The inexact version of these methods is derived. To illustrate the effectiveness of the proposed framework, several numerical examples are given.

中文翻译：

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求解复杂对称正定线性系统的两种不平衡TSCSP (LTSCSP)迭代方法

在本文中，我们在两尺度分裂（TSCSP）方法的基础上提出了两种新的不平衡方法（LTSCSP1 和 LTSCSP2），并表明在不增加任何额外参数的情况下，TSCSP 迭代方法的收敛速度可以在某些条件下得到提高。详细给出了新方法的收敛性分析。然后我们将获得准最优参数以最小化新方法的迭代矩阵的谱半径。导出了这些方法的不精确版本。为了说明所提出框架的有效性，给出了几个数值例子。