Algorithm 705; a FORTRAN-77 software package for solving the Sylvester matrix equation AXB(T) + CXD(T) = E

This paper documents a software package for solving the Sylvester matrix equation (1) AXB T + CXD T = e All quantities are real matrices; A and C are m x n ; B and D are m x n ; and X and E are m x n . The unknown is X . Two symmetric forms of Eq. (1) are treated separately for efficiency. They are the continuous-time symmetric Sylvester equation (2) AXE T + EXA T + C = 0 and the discrete time equation (3) AXA T + C = 0, for which A , E , and C is symmetric. The software also provides a means for estimating the condition number of these three equations. The algorithms employed are more fully described in an accompanying paper [3].