Generalized SOR Method for the Three-order Block Saddle Point Problems
高翔 1温瑞萍 1王川龙1
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作者信息
1. 太原师范学院智能优化计算与区块链技术山西省重点实验室,晋中 030619
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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.
Abstract
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.
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
Key words
saddle point problem/three-order block saddle point problem/SOR method/GSOR method/centered preconditioned method
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