Solution of the Sylvester matrix equation AXBT + CXDT = E

A software package has been developed to solve efficiently the Sylvester-type matrix equation <italic>AXB<supscrpt>T</supscrpt></italic> + <italic>CXD<supscrpt>T</supscrpt></italic> = <italic>E</italic>. 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.

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