TY - JOUR T1 - Optimal Approximate Solution of the Matrix Equation $AXB=C$ over Symmetric Matrices JO - Journal of Computational Mathematics VL - 5 SP - 543 EP - 552 PY - 2007 DA - 2007/10 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10347.html KW - Least-squares solution, Optimal approximate solution, Generalized singular value decomposition, Canonical correlation decomposition. AB -

Let $S_E$ denote the least-squares symmetric solution set of the matrix equation $AXB=C$, where $A$, $B$ and $C$ are given matrices of suitable size. To find the optimal approximate solution in the set $S_E$ to a given matrix, we give a new feasible method based on the projection theorem, the generalized SVD and the canonical correction decomposition.