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求解大型非对称线性系统的一种新的预处理方法

张秀梅1,2, 王川龙1,2   

  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

张秀梅, 王川龙. 求解大型非对称线性系统的一种新的预处理方法[J]. 数值计算与计算机应用, 2014, 35(1): 28-34.

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
针对大型稀疏非对称正定线性方程组,本文提出了新的预处理GMRES方法,并分析了谱半径和最优参数α的选取. 最后通过数值例子比较GMRES方法,HSS预处理和新的预处理GMRES方法,发现新的预处理方法具有更好的收敛率.
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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