线性互补问题的广义松弛两步模基矩阵分裂迭代法

将松弛策略引入到与线性互补问题等价的广义隐式定点迭代方程, 建立了求解线性互补问题的广义松弛两步模基矩阵分裂迭代法, 将已有的松弛两步模基矩阵分裂迭代法扩展到了更一般的情形; 当系数矩阵为H₊-矩阵时, 利用H₊-矩阵的特殊性质, 给出了新方法的收敛性分析.数值结果表明:依据迭代次数和CPU时间, 由新方法所导出的新的广义方法比已有的广义模基矩阵分裂迭代法和广义两步模基矩阵分裂迭代法更有效.

A General Relaxation Two-Sweep Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems

By introducing the relaxation strategies to the general implicit fixed-point equation, a general relaxation two-sweep modulus-based matrix splitting iteration method is established for linear complementarity problems, which extends the existing relaxation two-sweep modulus-based matrix splitting iteration method to more general cases. Based on some special properties of H₊-matrices, the convergence analyses are given when the system matrices are H₊-matrices. Numerical results verify that the new general methods derived from the proposed method are superior to the existing general modulus-based matrix splitting iteration methods and two-sweep modulus-based matrix splitting iteration methods in terms of the number of iteration steps and CPU time.