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.
出处
《成都理工大学学报（自然科学版）》
CAS
CSCD
北大核心
2003年第5期529-533,共5页
Journal of Chengdu University of Technology: Science & Technology Edition
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
unitary space
2 norm
generalized inreverse matrix
least square solution of least norm
regular equation
