摘要
3×3块鞍点问题作为一类特殊的线性方程组,其迭代方法的研究极具挑战性。基于经典的广义逐次超松弛(Generalized Successive Over Relaxation,GSOR)方法,针对3×3块大型稀疏鞍点问题,提出了三参数的中心预处理GSOR方法并讨论了其收敛性。同时,通过数值实验验证了新方法在计算花费方面优于中心预处理的Uzawa-Low方法。进一步地,还将新方法拓展到i×i块鞍点问题,提出了相应的GSOR类迭代框架,通过数值实验和数据分析,给出了选择较优i的初步建议。
As a special kind of linear system,the three-order block saddle point problem has challenging to study its iterative solution.Based on the classical generalized successive over relaxation(GSOR)method,the centered preconditioned GSOR method with three parameters for a class of three-order block large sparse saddle point problem is established and the conver-gence condition is discussed in this paper.Moreover,experimental results show that the new method has an advantage of computational cost over the centered preconditioned Uzawa-Low method.In addition,an extended one of the new method is provided,implementation details and analyses of corresponding framework about i-order block systems are shown,the blocking for saddle point problems are preliminarily proposed by some numerical results.
作者
高翔
温瑞萍
王川龙
GAO Xiang;WEN Ruiping;WANG Chuanlong(Shanxi Key Laboratory for Intelligent Optimization Computing and Block-chain Technology,Taiyuan Normal University,Jinzhong 030619)
出处
《工程数学学报》
CSCD
北大核心
2024年第5期808-824,共17页
Chinese Journal of Engineering Mathematics
基金
国家自然科学基金(12371381)
山西省自然科学基金(201901D211423).
关键词
鞍点问题
3×3块鞍点问题
SOR方法
GSOR方法
中心预处理方法
saddle point problem
three-order block saddle point problem
SOR method
GSOR method
centered preconditioned method
作者简介
高翔(1996—),女,硕士生.研究方向:矩阵数据分析和科学计算;通讯作者:温瑞萍,E-mail:wenrp@163.com。
