四川大学学报（自然科学版）2025，Vol.62Issue(3)：597-602,6.DOI:10.19907/j.0490-6756.240020
病态线性方程组的精细积分预处理共轭梯度求解法
A precise integral preconditioned conjugate gradient method for ill-conditioned linear systems
摘要
Abstract
Ill-conditioned linear equation system appears in many engineering problems.For ill-conditioned linear equation systems with large condition number,there is a big challenge to the numerical methods to keep high accuracy and high speed simultaneously.In this paper,the precise integral preconditioned conjugate gradient method is proposed.In this method,the precise integral method is combined with the conjugate gradi-ent method,where the former is used as the preconditioned method of the latter.Two numerical examples are utilized to verify the performance of the method.It is shown that the method can significantly reduce the com-putational cost and keep high accuracy,thus is an effective method for the ill-conditioned linear equation sys-tems.关键词
病态线性方程组/精细积分法/共轭梯度法/条件数Key words
Ill-conditioned linear system/Precise integration method/Conjugate gradient method/Condition number分类
数理科学引用本文复制引用
曾鑫,张世全..病态线性方程组的精细积分预处理共轭梯度求解法[J].四川大学学报（自然科学版）,2025,62(3):597-602,6.基金项目
四川省自然科学基金(2023NSFSC0075) （2023NSFSC0075）
