一种求解鞍点问题的改进Uzawa-PSS方法  

An Improved Uzawa-PSS Method for to Solve Point Problems

作　　者：沈海龙[1] 李红丽[1] 邵新慧[1] SHEN Hai-long;LI Hong-li;SHAO Xin-hui(School of Sciences,Northeastern University,Shenyang 110819,China)

机构地区：[1]东北大学理学院,辽宁沈阳110819

出　　处：《东北大学学报（自然科学版）》2019年第5期756-760,共5页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(11371081);辽宁省自然科学基金资助项目(20170540323)

摘　　要：主要针对非Hermitian鞍点问题,在已有Uzawa-PSS方法基础上构建了一种改进的Uzawa-PSS迭代法,其主要求解思想是在Uzawa-PSS方法的每一步迭代中需求解系数矩阵αI+P和αI+S的两个线性子系统.第一个子系统可用CG方法求解,但第二个子系统求解很困难.改进算法采用单步PSS迭代法逼近x_(k+1),然后用新方法分别求解了非奇异和奇异鞍点问题,并给出了相应的收敛性分析.数值仿真实验验证了改进Uzawa-PSS迭代法在迭代步数、占用CPU时间和相对残差上都有明显的优势.Aiming at the non-Hermitian saddle point problem,an improved Uzawa-PSS iteration method is constructed based on the existing Uzawa-PSS method.The main idea of the new method is to solve two linear subsystems in each iteration step of Uzawa-PSS method,whose coefficient matrices are α I+P and α I+S ,respectively.The first subsystem can be solved by CG method,but the second subsystem is very difficult to solve.The improved algorithm uses the single-step PSS iteration method to approximate the problem.Then the new method is used to solve the non-singular and singular saddle point problems respectively,and the corresponding convergence analysis is given.The numerical simulation also proves that the improved Uzawa-PSS iteration method has obvious advantages in iteration steps,CPU time and relative residuals.

关 键 词：鞍点问题 收敛 半收敛 奇异 非奇异 

分 类 号：O241.6[理学—计算数学]