一种解病态线性方程组的单参数迭代法  

New PCA Weighted Improvement Method of Morbid linear Equations

作　　者：薛正林 张莉[2] 吴开腾[2] XUE Zheng-lin ZHANG Li WU Kai-teng(Nanchong Twelfth Middle School, Nanchong, Sichuan 637000, China Key Laboratory of Numerical Simulation in the Sichuan Province, Neijiang Normal University, Neijiang, 641100, China)

机构地区：[1]南充十二中,四川南充637000 [2]内江师范学院四川省高等学校数值仿真重点实验室,四川内江641112

出　　处：《数学的实践与认识》2017年第10期255-261,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金青年基金(11502121);四川省教育厅创新团队计划项目(13TD00001);内江师范学院重点学科"计算数学"(0430101)

摘　　要：基于主元加权预处理的思想,针对病态线性方程组的病态性,通过引入参数构造了一种新的单参数迭代法,并给出了收敛性分析和条件数分析.单参数迭代法结构简单,计算量小,保证了求解过程的稳定性及高效性,数值实验的结果表明,算法对极其病态的线性方程组也有较好的精度.Based on the idea of principal component weighted pretreatment, for the illposed of ill conditioned linear equations, by introducing a parameter, a new single parameter iterative method was constructed. Besides, analysis of the convergence and condition number were given. Single parameter iterative method had the advantages of simple structure, small amount of calculation, to ensure stability and efficiency of the process of problem solving. Numerical experiment results shown that, algorithm for extremely morbid linear equations still kept good accuracy.

关 键 词：病态线性方程组 单参数迭代 收敛性 条件数 

分 类 号：O241.6[理学—计算数学]