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.
In order to reduce the condition number of the coefficient matrix of ill-conditioned linear equations,according to the equilibration thought for matrices,a 1-norm equilibration method was proposed to properly reduce the condition number of the matrix,and expanded to the norm equilibration methods. Then,the norm equilibration method together with the precise integration method was combined for solving ill-conditioned linear equations. The numerical results confirm that,the accuracy,efficiency and application scope of the preconditioned precise integration method for ill-conditioned linear equations all improve significantly（ the number of significant digits increases by more than 5 and the number of iterations decreases by about 15）. In these methods,the preconditioned precise integration method of 1-norm equilibration is the best.
作者
富明慧
李勇息
FU Minghui;LI Yongxi(Department of Applied Mechanics and Engineering, Sun Yat-sen University, Guangzhou 510275, P.R. China)
出处
《应用数学和力学》
CSCD
北大核心
2018年第4期462-469,共8页
Applied Mathematics and Mechanics
基金
国家自然科学基金(11672338
11502172)~~
关键词
范数
均衡
预处理
精细积分法
病态线性方程组
norm
equilibration
preconditioned technology
precise integration method
illconditioned linear equations
