## 留言板

 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.
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.

• 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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