线性最小二乘问题解法的理论分析  

THEORIES ANALYSIS OF LINEAR LEAST SQUARE METHOD

作　　者：何永斌[1] 范啸涛[2] 安红岩[2] 何果[3] 

机构地区：[1]攀枝花学院理学系,四川攀枝花617000 [2]成都理工大学信息管理学院 [3]交通银行成都分行

出　　处：《成都理工大学学报（自然科学版）》2003年第5期529-533,共5页Journal of Chengdu University of Technology: Science & Technology Edition

摘　　要：线性最小二乘问题的解法在数据拟合、测量平差、控制理论等方面均得到广泛的应用。针对复矩阵和酉空间这种最一般的情形,证明了线性最小二乘解的存在性,给出了线性最小二乘解的一般表示式和极小范数最小二乘解。另外还对正则化方程组的条件数进行了论证。许多结论与Euclid空间情况相近。The solution method of linear least square method is widely applied extensively in data fitting, the average of the erros in measurements, controlling theories, etc. The complex matrix and the unitary space are most general circumstances. This proves the existence of the linear least square solution and gives the general expression of the least square method and the least square solution of the least norm. In addition, it proves the regular equation's conditions number. Many conclusions of this paper are close to Euclid space.

关 键 词：酉空间 2范数 广义逆矩阵 极小范数最小二乘解 正则化方程组 

分 类 号：O241.5[理学—计算数学]