• 论文 •

### 求解大型非对称线性系统的一种新的预处理方法

1. 1. 太原理工大学数学学院, 太原 030024;
2. 太原师范学院工程科学计算重点实验室, 太原 030012
• 收稿日期:2013-04-07 出版日期:2014-03-15 发布日期:2014-03-14
• 基金资助:

中国自然科学资金（11071184，11371275）和 山西省自然科学资金（2010011006，2012011015-6）项目资助

Zhang Xiumei, Wang Chuanlong. A NEW PRECONDITIONER FOR ITERATIVELY SOLVING NON-HERMITIAN POSITIVE DEFINITE SYSTEMS[J]. Journal of Numerical Methods and Computer Applications, 2014, 35(1): 28-34.

### A NEW PRECONDITIONER FOR ITERATIVELY SOLVING NON-HERMITIAN POSITIVE DEFINITE SYSTEMS

Zhang Xiumei1,2, Wang Chuanlong1,2

1. 1. Taiyuan University of Technology, Institution of Mathematics, Taiyuan 030024, China;
2. Higher Education Key Laboratory of Engineering Science Computing, Taiyuan Normal University, Taiyuan 030012, China
• Received:2013-04-07 Online:2014-03-15 Published:2014-03-14

A new iterative method for solving a linear system with coefficient matrix being non- Hermitian positive definite is presented in this note. We analyze the spectral radius and the best possible choice of the parameter. Finally, numerical examples are given to compare GMRES method, preconditioned HSS method and the new preconditioned GMRES method, and show that the new preconditioned method has higher convergence rate.

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