摘要
通过矩阵的奇异值分解定理,得到矩阵方程ATXA=B的在加权范数下的最小二乘解和对称最小二乘解表达式,同时导出了在相应解集中与已知矩阵最佳逼近的最小二乘解。
Applying the singular value decomposition of matrices, we obtain the expression of the least squares solution and symmetric least squares solution of matrix equation A^TXA = B with weighted norm. Meanwhile, in the responding solution set of the matrix equation, we deprive the expression of the optimal approximation least squares solution to the given matrix.
出处
《湖南科技学院学报》
2006年第11期124-128,共5页
Journal of Hunan University of Science and Engineering
关键词
加权范数
最小二乘解
最佳逼近
奇异值分解
weighted norm
least square solution
optimal approximation
singular value decomposition
