DocumentCode
830746
Title
A Hessenberg-Schur method for the problem AX + XB= C
Author
Golub, G.H. ; Nash, S. ; Van Loan, C.
Author_Institution
Stanford University, Stanford, CA, USA
Volume
24
Issue
6
fYear
1979
fDate
12/1/1979 12:00:00 AM
Firstpage
909
Lastpage
913
Abstract
One of the most effective methods for solving the matrix equation 
is the Bartels-Stewart algorithm. Key to this technique is the orthogonal reduction of 
and 
to triangular form using the 
algorithm for eigenvalues. A new method is proposed which differs from the Bartels-Stewart algorithm in that is only reduced to Hessenberg form. The resulting algorithm is between 30 and 70 percent faster depending upon the dimensions of the matrices and . 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.
is the Bartels-Stewart algorithm. Key to this technique is the orthogonal reduction of and to triangular form using the algorithm for eigenvalues. A new method is proposed which differs from the Bartels-Stewart algorithm in that is only reduced to Hessenberg form. The resulting algorithm is between 30 and 70 percent faster depending upon the dimensions of the matrices and . 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.Keywords
Matrix equations; Arithmetic; Artificial intelligence; Computer errors; Computer science; Error analysis; Linear systems; Matrix decomposition; Roundoff errors; Testing; US Department of Energy;
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/TAC.1979.1102170
Filename
1102170
Link To Document