线性流形上矩阵方程B^TXB=D的加权最小二乘对称解和解的最佳逼近

The Weighted Least Squares Symmetric Solutions of Matrix Equation B^TXB=D and its Optimal Approximation on A Linear Manifold

本文利用矩阵的奇异值分解(SVD),给出了在一流形上矩阵方程BTXB=D的加权最小二乘对称解的通解表达式,并解决了加权最小二乘对称解的最佳逼近问题。

The expression of the weighted least squares symmetric solutions of matrix equation B^TXB = D on a linear manifold is derived by the use of matrix singular value decomposition （SVD）. Meanwhile, the optimal approximation solution is also obtained.