For solving large sparse linear complementarity problems effectively, by utilizing the parametric method, the acceleration strategy and the relaxation technique to the modulus-based matrix splitting (MMS) iteration method, we develop the accelerated relaxation MMS (ARMMS) iteration method, which generalizes the generalized accelerated MMS (GAMMS) and the relaxation MMS (RMMS) ones proposed recently. Meanwhile, it is proved that the ARMMS iteration method is convergent under proper restrictions when the system matrix is a positive definite matrix or an \(H_{+}\)-matrix. In addition, we also study the convergence properties of the ARM accelerated overrelaxation (ARMAOR) method. Numerical experiments show that the proposed iteration method is efficient, and it outperforms some existing ones with suitable choice of the parameter and matrix splitting.

为了有效地解决大型稀疏线性互补问题，通过利用参数方法，加速策略和基于模数的矩阵分裂（MMS）迭代方法的松弛技术，我们开发了加速松弛MMS（ARMMS）迭代方法，该方法概括了最近提出了广义加速MMS（GAMMS）和松弛MMS（RMMS）。同时，证明了当系统矩阵为正定矩阵或\（H _ {+} \）时，ARMMS迭代方法在适当的约束条件下收敛。-矩阵。此外，我们还研究了ARM加速过松弛（ARMAOR）方法的收敛特性。数值试验表明，该迭代方法是有效的，并且它优于同参数和矩阵分裂合适的选择一些现有的。