Solution of the Sylvester matrix equation AXB T + CXD T = E-Reference-Cited by-同舟云学术

Solution of the Sylvester matrix equation AXB T + CXD T = E

Published:1992-06 Issue:2 Volume:18 Page:223-231
ISSN:0098-3500
Container-title:ACM Transactions on Mathematical Software
language:en
Short-container-title:ACM Trans. Math. Softw.

Author:

Gardiner Judith D.¹,Laub Alan J.¹,Amato James J.²,Moler Cleve B.²

Affiliation:

1. Univ. of California, Santa Barbara

2. Univ. of New Mexico, Albuquerque

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.

Publisher

Association for Computing Machinery (ACM)

Subject

Applied Mathematics,Software

Link

https://dl.acm.org/doi/pdf/10.1145/146847.146929

Reference16 articles.

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3. A LINPACK-style condition estimator for the equation AX - XBr - C;BYERS R;IEEE Trans. Aut. Contr. AC~29,1984

4. The solution of the matrix equation AXB - CXD = E and (YA - DZ, YC - BZ) = (E, F);CHU K.-W.;Lin. Alg. Appl.,1987

5. An estimate for the condition number of a matrix SIAM J;CLINE A. K.;Numer. Anal.,1979

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