两步模系矩阵分裂算法求解弱非线性互补问题

Twostep Modulusbased Matrix Splitting Algorithms for Weakly Nonlinear Complementarity Problems

摘要:

考虑两步模系矩阵分裂算法求解弱非线性互补问题, 理论分析给出了当系数矩阵为正定矩阵或H+矩阵时迭代法的收敛性质和两步模系超松弛迭代法的参数选取范围. 数值实验表明, 两步模系矩阵分裂算法是行之有效的, 并在迭代步数和迭代时间上均优于模系矩阵分裂算法.

关键词:矩阵分裂; 两步模系算法; 弱非线性互补问题

Abstract:

wostep modulusbased matrix splitting algorithms are proposed to solve weakly nonlinear complementarity problems. Convergence theory is established when the system matrix is either positive definite or an H+matrix. Moreover, the choice of the parameters for twostep modulusbased successive overrelaxation methods is also discussed. Numerical experiments show that the proposed methods are efficient and better than the modulusbased matrix splitting methods in aspects of iteration steps and CPU time.

Key words:matrix splitting; twostep modulusbased algorithms; weakly nonlinear complementarity problems