Algorithm 705; a FORTRAN-77 software package for solving the Sylvester matrix equation AXBT+ CXDT= E

Abstract

This paper documents a software package for solving the Sylvester matrix equation (1)AXBT+CXDT=eAll quantities are real matrices;AandCaremxn;BandDaremxn; andXandEaremxn. The unknown isX. Two symmetric forms of Eq. (1) are treated separately for efficiency. They are the continuous-time symmetric Sylvester equation (2)AXET+EXAT+C= 0 and the discrete time equation (3)AXAT+C= 0, for whichA,E, andCis 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].