Using the GSVD and the lifting technique to find reflexive and anti-reflexive solutions of

The generalized singular value decomposition (GSVD) and the lifting technique combined with the Kronecker product are exploited to find reflexive and anti-reflexive (with respect to a generalized { k + 1 } -reflection matrix P ) solutions of the matrix equation A X B = C . The computational cost of the presented algorithm is studied and several numerical examples are presented.