求解大规模稀疏垂直线性互补问题的二步模基并行算法  

A TWO-STEP MODULUS-BASED PARALLEL METHOD FOR SOLVING LARGE SPARSE VERTICAL LINEAR COMPLEMENTARITY PROBLEMS

作　　者：郑华 温海斌 卢晓平[2] Zheng Hua;Wen Haibin;Lu Xiaoping(School of Mathematics and Statistics,Shaoguan University,Shaoguan 512005,China;School of Computer Science and Engineering,Macao University of Science and Technology,Macao 999078,China)

机构地区：[1]韶关学院数学与统计学院,韶关512005 [2]澳门科技大学计算机科学与工程学院,中国澳门999078

出　　处：《数值计算与计算机应用》2023年第4期350-367,共18页Journal on Numerical Methods and Computer Applications

基　　金：广东省普通高校科研创新团队项目(2021KCXTD052);广东省普通高校基础研究与应用基础研究重点项目(2018KZDXM065);澳门科学技术发展基金项目(0096/2022/A);韶关市科技计划项目(210716094530390)资助。

摘　　要：针对大规模垂直线性互补问题的求解,运用二步多分裂技术构建了二步模基矩阵同步多分裂并行迭代方法,新方法可以看成是已有文献中模基矩阵同步多分裂迭代法和二步模基矩阵分裂迭代法的推广.进一步地,在系统矩阵为H+矩阵的假设下,给出算法收敛性分析,得到了参数矩阵的收敛域,推广了已有算法的收敛性结果.最后,在OpenMP框架下针对已有文献中的两个数值例子给出了数值试验,试验结果展示了二步多分裂技术能提升已有方法的计算效率.In the paper,for solving large sparse vertical linear complementarity problems,a two-step modulus-based matrix synchronous multisplitting parallel iteration method is construct-ed by using two-step multisplitting technique.The new method can be viewed as a gener-alization of the modulus-based matrix synchronous multisplitting iterative method and the two-step modulus-based matrix splitting iterative method in the existing literatures.Fur-thermore,under the assumption that the system matrices are H+-matrices,the convergence analysis of the proposed method is given,and the convergence domain of the parameter matrix is obtained,which extends the convergence results of the existing methods.Finally,numerical experiments are carried out under the OpenMP framework for two numerical examples in the existing literatures.Numerical results show that the two-step multisplitting technique can improve the computational efficiency of the existing methods.

关 键 词：垂直线性互补问题 二步方法 多分裂 并行 

分 类 号：O151.21[理学—数学]