求解鞍点问题的广义正定和反Hermitian分裂方法

计算机工程与科学

求解鞍点问题的广义正定和反Hermitian分裂方法

董贝贝，鲍亮

（华东理工大学理学院，上海 200237）

收稿日期:2018-12-11 修回日期:2019-04-08 出版日期:2019-09-25 发布日期:2019-09-25

A generalized positive-definite and skew-Hermitian

splitting iteration method for saddle point problems

DONG Bei-bei,BAO Liang

（School of Science,East China University of Science and Technology,Shanghai 200237,China）

Received:2018-12-11 Revised:2019-04-08 Online:2019-09-25 Published:2019-09-25

摘要/Abstract

摘要：

探讨了如何求解大型稀疏鞍点问题，给出了一种基于正定分裂的广义正定和反Hermitian分裂(GPSS)方法。该方法首先利用矩阵的正定分裂，构造出鞍点矩阵的2种分裂格式；然后利用这2种分裂格式构造出GPSS迭代；接着给出了迭代收敛的充要条件。最后进行了数值对比实验，实验结果表明,GPSS比正定和反Hermitian分裂(PSS)和Hermitian和反Hermitian分裂(HSS)方法更有效。

关键词: 鞍点问题, GPSS, 收敛性, 正定分裂

Abstract:

We propose a generalized positive-definite and skew-Hermitian splitting method to solve the large sparse saddle point problems based on the positive-definite splitting. The method first uses the positive-definite splitting of matrix to construct two splitting forms of the saddle-point matrix. Then, the two splitting formats are used to construct the GPSS iteration. Thirdly, the necessary and sufficient conditions for the iteration convergence are given. Finally, some numerical comparison experiments are carried out and the results show that the GPSS is more effective than "the positive-definite and skew-Hermitian splitting" (PSS) method and "the Hermitian and skew-Hermitian splitting" (HSS) method.

Key words: saddle-point problem, generalization of the positive-definite and skew-Hermitian splitting (GPSS), convergence, positive splitting

董贝贝，鲍亮. 求解鞍点问题的广义正定和反Hermitian分裂方法[J]. 计算机工程与科学.

DONG Bei-bei,BAO Liang.

A generalized positive-definite and skew-Hermitian

splitting iteration method for saddle point problems

[J]. Computer Engineering & Science.

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