应用数学和力学2018，Vol.39Issue(4)：462-469,8.DOI:10.21656/1000-0887.380206
求解病态线性方程组的预处理精细积分法
A Preconditioned Precise Integration Method for Solving Ill-Conditioned Linear Equations
摘要
Abstract
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.关键词
范数/均衡/预处理/精细积分法/病态线性方程组Key words
norm/equilibration/preconditioned technology/precise integration method/ill-conditioned linear equations分类
数理科学引用本文复制引用
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):462-469,8.基金项目
The National Natural Science Foundation of China(11672338 （）
11502172)国家自然科学基金(11672338 （）
11502172) （）
