In this paper, we present some novel observations for the semidefinite linear complementarity problems, abbreviated as SDLCPs. Based on these new results, we establish the modulus-based matrix splitting iteration methods, which are obtained by reformulating equivalently SDLCP as an implicit fixed-point matrix equation. The convergence of the proposed modulus-based matrix splitting iteration methods has been analyzed. Numerical experiments have shown that the modulus-based iteration methods are effective for solving SDLCPs.

中文翻译：

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半定线性互补问题矩阵分裂迭代算法的收敛性分析

在本文中，我们提出了关于半定线性互补问题（缩写为SDLCP）的一些新发现。基于这些新结果，我们建立了基于模量的矩阵分解迭代方法，该方法是通过将SDLCP等效地重新公式化为隐式定点矩阵方程而获得的。分析了所提出的基于模量的矩阵分裂迭代方法的收敛性。数值实验表明，基于模量的迭代方法对于求解SDLCP是有效的。