有关一类H_+矩阵线性互补问题的修正模系矩阵分裂迭代方法

A Modified General Modulus-based Matrix Splitting Method for Linear Complementarity Problems of H_+-matrices

我们在本文建立了一类H+矩阵线性互补问题的修正模系矩阵分裂迭代方法并且给出了其收敛性分析.此外,我们也考虑了在给定方法下的最优参数选取问题.我们得出的修正方法是对[Xu W W, Liu H, A modified general modulus-based matrix splitting method for linear complementarity problems of H-matrices, Linear Algebra. Appl., 2014, 458:626-637]中方法2.1的一个修正.同时,我们也对[Xu W W,Modified modulus-based matrix splitting iteration methods for linear complementarity problems, Numer. Linear Algebra. Appl., 2015, 5:748-760]中方法3.1和方法3.2有关解的等价性证明作了补充说明.最后,我们给出的数值例子也表明了修正方法的有效性.

In this paper we establish a modified general modulus-based matrix splitting iteration method for solving the large sparse linear complementarity problems of H_+-matrix and present the convergence analysis. In addition, the optimal parameters are considered under the given methods and we supplement the proof of equivalence of(z,r) from Methods3.1 and 3.2 in [2] and the solution of the original linear complementary problem LCP(q, A).Finally, we give a numerical example, which illustrates that the modified method is efficient.