The least-squares solutions of two kinds of matrix equations

In this paper, the least-squares solutions to the matrix equations $AX_{1}+X_{2}A^{\ast}+BY_{1}C+C^{\ast}Y_{2}B^{\ast}=E$ and $A^{\ast}X+X^{\ast}A+B^{\ast}YC+C^{\ast}Y^{\ast}B=D$ are discussed. By using the singular value decompositions and the canonical correlation decompositions (CCDs) of some matrices, the explicit expressions of the least-squares solutions to the above matrix equations are provided.