3 Algorithm
For complex matrix equations (1), in which\(A,C\in C^{m\times n},\ B,D\in C^{n\times s}\ ,E,F\in C^{m\times s}\).
the following Theorem 1, Corollary 1 and Corollary 2, we propose the
following algorithms for solving the Hermitian minimum norm least square
solution, the real symmetric minimum norm least square solution and the
real dissymmetric minimum norm least square solution of (1).
Algorithm 1(solving the Hermitian minimum norm least square
solution of (1) )
(1) Input\(\ A,\ B\ ,C,D,E,F\ H,K,G\),
(2)
Form\(\text{\ A}^{R},C^{R},\text{\ B}_{c}^{R},D_{c}^{R},E_{c}^{R},\text{\ F}_{c}^{R},\)
(3) Calculat\(\ \par
\begin{pmatrix}\text{ves}_{S}\left(X_{0}\right)\\
\text{ves}_{A}\left(X_{1}\right)\\
\end{pmatrix}={[\left(\frac{{{(B}_{c}^{R})}^{T}\otimes A^{R}}{\left(D_{c}^{R})^{T}\otimes C^{R}\right)}\right)HKG]}^{+}\left(\frac{E_{c}^{R}}{F_{c}^{R}}\right)\).
Algorithm 2 (solving the real symmetric minimum norm least
square solution of (1))
(1) Input\(\ A,\ B\ ,C,D,E,F\ H,V,K_{n}\),
(2) Form \(A^{R},C^{R},B_{c}^{R},D_{c}^{R},E_{c}^{R},F_{c}^{R},\)
(3)
Calculat\(\text{\ ves}_{S}\left(X_{0}\right)={[\left(\frac{{{(B}_{c}^{R})}^{T}\otimes A^{R}}{\left(D_{c}^{R})^{T}\otimes C^{R}\right)}\right)\text{HV}K_{n}]}^{+}\left(\frac{E_{c}^{R}}{F_{c}^{R}}\right)\).
Algorithm 3 (solving the real dissymmetric minimum norm least
square solution of (1))
(1) Input\(\ A,\ B\ ,C,D,E,F\ H,V,L_{n}\),
(2) Form \(A^{R},C^{R},B_{c}^{R},D_{c}^{R},E_{c}^{R},F_{c}^{R}\),
(3)
Calculat\(\ \text{ves}_{A}\left(X_{0}\right)={[\left(\frac{{{(B}_{c}^{R})}^{T}\otimes A^{R}}{\left(D_{c}^{R})^{T}\otimes C^{R}\right)}\right)\text{HV}L_{n}]}^{+}\left(\frac{E_{c}^{R}}{F_{c}^{R}}\right)\).