大规模加权总体最小二乘问题的迭代算法  

An iterative method for large-scale weighted total least squares problems

作　　者：张福到 刘巧华[1] 

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2016年第4期499-507,共9页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11001167)

摘　　要：变量含误差(EIV)模型常常用加权总体最小二乘方法估计参数,但是当系数矩阵为大规模稀疏阵时,该算法会花费较大的计算量和存储空间.为了控制存储和计算量,提出了一种基于加权Rayleigh商的迭代算法.数值算例表明,与经典的总体最小二乘算法相比,新算法减少了计算量和存储空间,并且能更好地估计参数.The weighted total least squares method is typical for solving the errors- in-variables （EIV） model. However, when the coefficient matrix is large, the method might be expensive in computation and storage cost. For reducing the storage and computation cost, a weighted Rayleigh quotient iteration method is presented. Numerical experiments show that the new method produces a better estimate than the standard total least squares method.

关 键 词：变量含误差模型 加权总体最小二乘问题 加权Rayleigh商迭代 

分 类 号：O241.6[理学—计算数学]