求解加权线性最小二乘问题的预处理迭代方法  

Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems

作　　者：沈海龙[1,2] 邵新慧[1] 张铁[1] 

机构地区：[1]东北大学理学院,沈阳110004 [2]东北大学信息科学与工程学院,沈阳110004

出　　处：《应用数学和力学》2012年第3期357-365,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(11071033);中央高校基本业务费资助项目(090405013)

摘　　要：给出了求解一类加权线性最小二乘问题的预处理迭代方法,也就是预处理的广义加速超松弛方法(GAOR),得到了一些收敛和比较结果.比较结果表明当原来的迭代方法收敛时,预处理迭代方法会比原来的方法具有更好的收敛率.而且,通过数值算例也验证了新预处理迭代方法的有效性.The preconditioned iterative methods for solving linear systems based on a class of weighted linear least square problems were proposed,which were the preconditioned generalized accelerated overrelaxation（GAOR） methods.Some convergence and comparison results were obtained.The comparison results show that the convergence rate of the preconditioned iterative methods is indeed better than the rate of the original methods,whenever the original methods are convergent.Furthermore,effectiveness of the new preconditioned methods is shown by numerical experiment.

关 键 词：预处理因子 GAOR方法 加权最小二乘问题 收敛 

分 类 号：O151.21[理学—数学] O241.6[理学—基础数学]