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求解病态线性方程组的预处理精细积分法

富明慧 李勇息

富明慧, 李勇息. 求解病态线性方程组的预处理精细积分法[J]. 应用数学和力学, 2018, 39(4): 462-469. doi: 10.21656/1000-0887.380206
引用本文: 富明慧, 李勇息. 求解病态线性方程组的预处理精细积分法[J]. 应用数学和力学, 2018, 39(4): 462-469. doi: 10.21656/1000-0887.380206
FU Minghui, LI Yongxi. A Preconditioned Precise Integration Method for Solving Ill-Conditioned Linear Equations[J]. Applied Mathematics and Mechanics, 2018, 39(4): 462-469. doi: 10.21656/1000-0887.380206
Citation: FU Minghui, LI Yongxi. A Preconditioned Precise Integration Method for Solving Ill-Conditioned Linear Equations[J]. Applied Mathematics and Mechanics, 2018, 39(4): 462-469. doi: 10.21656/1000-0887.380206

求解病态线性方程组的预处理精细积分法

doi: 10.21656/1000-0887.380206
基金项目: 国家自然科学基金(11672338;11502172)
详细信息
    作者简介:

    富明慧(1966—),男,教授,博士,博士生导师(通讯作者. E-mail: stsfmh@mail.sysu.edu.cn).

  • 中图分类号: O242

A Preconditioned Precise Integration Method for Solving Ill-Conditioned Linear Equations

Funds: The National Natural Science Foundation of China(11672338;11502172)
  • 摘要: 为降低病态线性方程组系数矩阵的条件数,根据矩阵行(列)均衡的思想,提出行(列)的1范数均衡法,并扩展为范数均衡法.然后,将范数均衡法与精细积分法相结合,给出求解病态线性方程组的范数均衡预处理精细积分法.数值结果表明,经过范数均衡预处理后精细积分法求解病态方程的精度(有效数字增加5个以上)和效率(迭代次数降低15次左右)均能得到显著提高,适用范围在一定程度上也有所扩展.在上述方法中,以1范数均衡预处理精细积分法效果最为显著.
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出版历程
  • 收稿日期:  2017-07-25
  • 修回日期:  2017-11-08
  • 刊出日期:  2018-04-15

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