关于矩阵方程AX+YB=C反问题的极小Frobenius范数对称解

The Minimum Frobenius Norm Solution of a Inverse Problem for Matrix Equation AX+YB=C

在线性约束下矩阵束最佳逼近问题中,对给定的条件做一改变,解决了一个矩阵束最佳逼近问题。设A、B、C都是m×n阶矩阵,当A和B满足同时奇异值分解(SSVD)时,解决了一个关于X,Y的矩阵方程AX+YB=C的反问题:即求X∈SRn×n,Y∈SRm×m,使得满足||AX+YB-C||F=min,得到了其Frobenius范数对称解。

An Optimal Opproximation of matrix-fibres under linear constrains was solved with the modifying of the condition. The inverse problem for matrix equation of X, Y,AX ＋ YB = C（A,B and C are m × n matrixies）was solved , when A and B satisfied the samesingular value decomposition （SSVD）. We sought the symmetric matrix X ∈ SRn ^n×n, Y ∈ SR^m×m, to satisfy ‖AX＋YB-C‖ F = min ,and obtained the minimum-Frobenius-norm symmetric solution.