精细积分阻尼谱修正迭代法在病态线性方程组中的应用  

Iteration method by correcting eigenvalue with damping factor based on precise integration for ill-conditioned linear system

作　　者：覃有堂 林贤坤[2] 覃柏英[2] 

机构地区：[1]柳州市第一职业技术学校,广西柳州545616 [2]广西科技大学汽车与交通学院,广西柳州545006

出　　处：《广西科技大学学报》2017年第3期1-8,15,共9页Journal of Guangxi University of Science and Technology

基　　金：广西自然科学基金(2012GXNSFAA053208);广西教育厅科研项目(200103YB105)资助

摘　　要：基于谱修正迭代法,引入阻尼因子和结合精细积分的矩阵求逆,提出了精细积分阻尼谱修正迭代法,并将其应用于病态线性方程组的求解.通过4个经典算例,探讨矩阵的精细积分求逆对阻尼谱修正迭代法求解病态线性方程组的影响.结果表明,矩阵的精细积分求逆可提高阻尼谱修正迭代法求解病态线性方程组的精度.再通过两个经典算例,探讨了精细积分阻尼谱修正迭代法在高维病态线性方程组中的应用.结果表明,该算法也可提高高维病态线性方程组求解的精度.To improve the performance of the iteration method by correcting eigenvalue （IMCE）, a damping factor and the precise integration method are introduced to IMCE. Thus an iteration method by correcting characteristic value with damping factor based on the precise integration method （PIM-DIMCE） is presented in the paper. Four classical examples are used to discuss the influence of the precise integration method （PIM） when IMCE solves the ill conditioned linear system （ICES）. The results show that PIM can improve the accuracy of IMCE for solving ICLS. Meanwhile, two classical examples are used to discuss the performance of PIM-DIMCE for solving the high dimensional ICLS. High computation accuracy is achieved as well when solving the high dimensional ICLS.

关 键 词：精细积分 阻尼因子 谱修正迭代法 

分 类 号：O241.6[理学—计算数学] O151.2[理学—数学]