Solution of the Sylvester matrix equation AXBT + CXDT = E

Authors:
Judith D. Gardiner;Alan J. Laub;James J. Amato;Cleve B. Moler
Affiliations:
Univ. of California, Santa Barbara;Univ. of California, Santa Barbara;Univ. of New Mexico, Albuquerque;Univ. of New Mexico, Albuquerque
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
1992

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Abstract

A software package has been developed to solve efficiently the Sylvester-type matrix equation AXBT + CXDT = 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.