中心对称线性互补问题的一类迭代算法

The Iterative Methods for the Centrosymmetric Linear Complementarity Problem

在考虑中心对称矩阵可约性的基础上,运用矩阵分裂理论,分别提出求解中心对称线性互补问题的对三角分裂松驰迭代算法和对三角分裂松驰迭代算法,并对2种算法进行收敛分析和数值实验.结果表明,当线性互补问题的系数矩阵对角元为正的H-矩阵时,2种算法都全局收敛,所得迭代阵的谱半径都为0.5,比传统的Jacobi分裂迭代算法和Gauss-seidel迭代算法的收敛速度都好.新算法节约了计算量与计算机的存贮空间,较大地提高了计算效率.

A relaxed opposite triangular splitting iterative algorithm Ⅰand a relaxed opposite triangular splitting iterative algorithm Ⅱ for solving centrosymmetric linear complementarity problem are given. In particular, we establish the global convergence theory of the algorithms when the system matrix of the centrosymmetric linear complementarity problem is an H-matrix. These algorithms,originated mainly from the reducibility of the centrosymmetric matrices,are aimed at reduction of the computation. The simulation examples show that these algorithms are efficient.