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非Hermite线性方程组的若干预处理迭代算法

张迎春 李英 肖曼玉 谢公南

张迎春, 李英, 肖曼玉, 谢公南. 非Hermite线性方程组的若干预处理迭代算法[J]. 应用数学和力学, 2019, 40(3): 237-249. doi: 10.21656/1000-0887.390222
引用本文: 张迎春, 李英, 肖曼玉, 谢公南. 非Hermite线性方程组的若干预处理迭代算法[J]. 应用数学和力学, 2019, 40(3): 237-249. doi: 10.21656/1000-0887.390222
ZHANG Yingchun, LI Yin, XIAO Manyu, XIE Gongnan. Some Preconditioning Iterative Algorithms for Non-Hermitian Linear Equations[J]. Applied Mathematics and Mechanics, 2019, 40(3): 237-249. doi: 10.21656/1000-0887.390222
Citation: ZHANG Yingchun, LI Yin, XIAO Manyu, XIE Gongnan. Some Preconditioning Iterative Algorithms for Non-Hermitian Linear Equations[J]. Applied Mathematics and Mechanics, 2019, 40(3): 237-249. doi: 10.21656/1000-0887.390222

非Hermite线性方程组的若干预处理迭代算法

doi: 10.21656/1000-0887.390222
基金项目: 国家自然科学基金(51676163)
详细信息
    作者简介:

    张迎春(1992—),女,博士生(E-mail: zhangyingchun@mail.nwpu.edu.cn);谢公南(1980—),男,教授,博士,博士生导师(通讯作者. E-mail: xgn@nwpu.edu.cn).

  • 中图分类号: O246

Some Preconditioning Iterative Algorithms for Non-Hermitian Linear Equations

Funds: The National Natural Science Foundation of China(51676163)
  • 摘要: 非Hermite线性方程组在科学和工程计算中有着重要的理论研究意义和使用价值,因此如何高效求解该类线性方程组,一直是研究者所探索的方向.通过提出一种预处理方法,对非Hermite线性方程组和具有多个右端项的复线性方程组求解的若干迭代算法进行预处理,旨在提高原算法的收敛速度.最后通过数值试验表明,所提出的若干预处理迭代算法与原算法相比较,预处理算法迭代次数大大降低,且收敛速度明显优于原算法.除此之外,广义共轭A-正交残量平方法(GCORS2)的预处理算法与其他算法相比,具有良好的收敛性行为和较好的稳定性.
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出版历程
  • 收稿日期:  2018-08-23
  • 修回日期:  2018-09-02
  • 刊出日期:  2019-03-01

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