• 论文 •

### 广义鞍点问题的改进的类SOR算法

1. 1. 南京师范大学数学科学学院, 南京 210023;
2. 中国人民解放军陆军工程大学基础部, 南京 211101;
3. 南京信息工程大学数学与统计学院, 南京 210044;
4. 北京航空航天大学数学科学学院, 北京 100191
• 收稿日期:2018-03-07 出版日期:2020-02-15 发布日期:2020-02-15
• 基金资助:

国家自然科学基金（11625105，11926358，11871279，11571178，11801279），江苏省自然科学基金（BK2018078），南京信息工程大学科研启动基金（2017r059）.

Zhang Chun, Jia Zehui, Cai Xingju, Han Deren. AN IMPROVED SOR-TYPE ALGORITHM FOR SLOVING GENERALIZED SADDLE-POINT PROBLEMS[J]. Mathematica Numerica Sinica, 2020, 42(1): 39-50.

### AN IMPROVED SOR-TYPE ALGORITHM FOR SLOVING GENERALIZED SADDLE-POINT PROBLEMS

Zhang Chun1,2, Jia Zehui3, Cai Xingju1, Han Deren4

1. 1. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China;
2. Department of Basic Courses, The PLA Army Engineering University, Nanjing 211101, China;
3. School of Mathematics and Statistics, Nanjing University of Information Science&Technology, Nanjing 210044, China;
4. School of Mathematical Sciences, Beihang University, Beijing 100191, China
• Received:2018-03-07 Online:2020-02-15 Published:2020-02-15

For the generalized saddle point problem, we develop an improved class of successive over relaxation algorithms. Under mild conditions, we prove its convergence and establish its linear rate of convergence. While, as the classical methods, it needs to solve some linear system of equations approximately to get the next iterate, the flexibility in choosing the involved matrices makes the subproblems easy or even to have closed form solutions, which leads the algorithm to be an efficient one. Preliminary numerical results show the effectiveness of the new method.

MR(2010)主题分类:

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