病态代数系统求解的精细迭代方法  

Precise Iterative Refinement of Solution for Ill-Conditioned Systems of Linear Algebraic Equations

作　　者：张文志[1] 黄培彦[1] 

机构地区：[1]华南理工大学土木与交通学院,广州510640

出　　处：《应用数学和力学》2013年第7期736-741,共6页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(重点)资助项目(11132004;51078145)

摘　　要：提出了病态代数系统求解的精细迭代方法.首先利用一个小参数对病态矩阵加以改良,将原病态系统的求解问题转化为该改良系统的求解问题.然后利用精细积分法给出了改良矩阵求逆的高精度方法.该方法具有高精度、高效率的优点,且对改良参数的适应性较好,具有良好的应用前景.理论和数值分析证明了该方法的有效性.A precise iterative refinement of solution for ill-conditioned systems of linear alge- braic equations was proposed. First, the ill-conditioned matrix was improved through introduc- tion of a small parameter, and then via the precise integration method, a highly precise method was provided for the inversion of the improved matrix. Both the theoretical convergence analy- sis and numerical examples show the efficiency and accuracy of the method.

关 键 词：病态代数系统 精细积分法 迭代算法 

分 类 号：O241.5[理学—计算数学] O302[理学—数学]