In this paper, to economically and fast solve the linear complementarity problem, based on a new equivalent fixed-point form of the linear complementarity problem, we establish a class of new modulus-based matrix splitting methods, which is different from the previously published works. Some sufficient conditions to guarantee the convergence of this new iteration method are presented. Numerical examples are offered to show the efficacy of this new iteration method. Moreover, the comparisons on numerical results show the computational efficiency of this new iteration method advantages over the corresponding modulus method, the modified modulus method and the modulus-based Gauss–Seidel method.

在本文中，为了经济、快速地解决线性互补问题，我们基于线性互补问题的一种新的等效不动点形式，建立了一类新的基于模数的矩阵分裂方法，这与之前发表的作品不同. 给出了保证这种新迭代方法收敛的一些充分条件。提供了数值例子来展示这种新迭代方法的有效性。此外，数值结果的比较表明，这种新迭代方法的计算效率优于相应的模数法、修正模数法和基于模数的高斯-赛德尔法。