求解病态线性方程组的精细积分新主元加权迭代法  

A precise integration and new principal element weighted iterative method for solving ill-conditioned linear equations

作　　者：郝强[1] 王慧蓉[1] 常金勇 HAO Qiang;WANG Huirong;CHANG Jinyong(Department of Mathematics,Changzhi University,Changzhi 046011,China;College of Information and Control Engineering,Xi’an University of Architecture and Technology,Xi’an 710055,China)

机构地区：[1]长治学院数学系,山西长治046011 [2]西安建筑科技大学信息与控制工程学院,陕西西安710055

出　　处：《安徽大学学报（自然科学版）》2022年第3期63-67,共5页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(61602061);山西省高校教改项目(J2015111);长治学院校级科研项目(zc2017006)。

摘　　要：在精细积分法的基础上,通过构造一个特殊的加权矩阵,并将其应用于主元加权迭代法.提出了一种将主元加权迭代法与精细积分法相结合的求解病态方程组的新算法,并用该算法求解两个经典算例.实验结果表明,该算法在求解精度和迭代次数上都有明显提升,是一种可以有效求解病态方程组近似解的新算法.Based on the idea of precise integration method,a special weighted matrix was constructed and applied to the principal element weighted iterative method.A new algorithm for solving ill-conditioned equations was proposed by combining principal element weighted iterative method with precise integration method.Furthermore,the numerical results from two classic experiments showed that the proposed method had significant improvement in accuracy and iteration number,and it was an effective algorithm for solving ill-conditioned equations.

关 键 词：精细积分法 主元加权迭代法 病态线性方程组 

分 类 号：O242[理学—计算数学]