Solution of the Sylvester matrix equation AXB ^<i>T</i> + CXD ^<i>T</i> = E

Abstract

A software package has been developed to solve efficiently the Sylvester-type matrix equation AXB T + CXD T = E . A transformation method is used which employs the QZ algorithm to structure the equation in such a way that it can be solved columnwise by a back substitution technique. The algorithm is an extension of the Bartels-Stewart method and the Hessenberg-Schur method. The numerical performance of the algorithms and software is demonstrated by application to near-singular systems.