HESSENBERG-SCHUR METHOD FOR THE PROBLEM AX+XB=C

One of the most effective methods for solving the matrix equation AX +XB= C is the Bartels-Stewart algorithm. Key to this technique is the orthogonal reduction of A and B to triangular form using the QR algorithm for eigenvalues. A new method is proposed which differs from the Bartels-Stewart a1gorithm in that A is only reduced to Hessenberg form. The resulting algorithm is between 30 and 70 percent faster depending upon the dimensions of the matrices A and B. The stability of the new method is demonstrated through a roundoff error analysis and supported by numerical tests. Finally, it is shown how the techniques described can be applied and generalized to other matrix equation problems. Copyright © 1979 by The Institute of Electricala and Electronics Engineers Inc.