Comptes Rendus
no. 11
Numerical analysis
Solving the mixed Sylvester matrix equations by matrix decompositions
[Résolution d'équations matricielles de Sylvester mixtes par décompositions de matrices]

Présenté par : Olivier Pironneau

Yongxin Yuan1
1 School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, PR China
Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 1053-1059.

En utilisant les décompositions en valeurs singulières généralisées (GSVDs) de couples de matrices, on établit une condition nécessaire et suffisante de résolubilité d'équations de Sylvester mixtes et on donne une représentation explicite de la solution générale. On étudie également la solution de norme minimale d'équations matricielles.

By applying the generalized singular-value decompositions (GSVDs) of matrix pairs, a necessary and sufficient solvability condition for mixed Sylvester equations is established, the explicit representation of the general solution is given. Also, the minimum-norm solution of the matrix equations is discussed.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.08.010
Yongxin Yuan 1

1 School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, PR China 
@article{CRMATH_2015__353_11_1053_0,
     author = {Yongxin Yuan},
     title = {Solving the mixed {Sylvester} matrix equations by matrix decompositions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1053--1059},
     publisher = {Elsevier},
     volume = {353},
     number = {11},
     year = {2015},
     doi = {10.1016/j.crma.2015.08.010},
     language = {en},
}
TY  - JOUR
AU  - Yongxin Yuan
TI  - Solving the mixed Sylvester matrix equations by matrix decompositions
JO  - Comptes Rendus. Mathématique
PY  - 2015
SP  - 1053
EP  - 1059
VL  - 353
IS  - 11
PB  - Elsevier
DO  - 10.1016/j.crma.2015.08.010
LA  - en
ID  - CRMATH_2015__353_11_1053_0
ER  - 
%0 Journal Article
%A Yongxin Yuan
%T Solving the mixed Sylvester matrix equations by matrix decompositions
%J Comptes Rendus. Mathématique
%D 2015
%P 1053-1059
%V 353
%N 11
%I Elsevier
%R 10.1016/j.crma.2015.08.010
%G en
%F CRMATH_2015__353_11_1053_0
Yongxin Yuan. Solving the mixed Sylvester matrix equations by matrix decompositions. Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 1053-1059. doi : 10.1016/j.crma.2015.08.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.08.010/

[1] J.K. Baksalary; R. Kala The matrix equation AX−YB=C, Linear Algebra Appl., Volume 25 (1979), pp. 41-43

[2] A. Ben-Israel; T.N.E. Greville Generalized Inverses: Theory and Applications, Springer, New York, 2003

[3] G.H. Golub; C.F. Van Loan Matrix Computations, The Johns Hopkins University Press, Baltimore, MD, USA, 1983

[4] S.G. Lee; Q.P. Vu Simultaneous solutions of matrix equations and simultaneous equivalence of matrices, Linear Algebra Appl., Volume 437 (2012), pp. 2325-2339

[5] Y.-H. Liu Ranks of solutions of the linear matrix equation AX+YB=C, Comput. Math. Appl., Volume 52 (2006), pp. 861-872

[6] C.C. Paige; M.A. Saunders Towards a generalized singular value decomposition, SIAM J. Numer. Anal., Volume 18 (1981), pp. 398-405

[7] G.W. Stewart Computing the CS-decomposition of a partitioned orthogonal matrix, Numer. Math., Volume 40 (1982), pp. 297-306

[8] Q.-W. Wang; Z.-H. He Solvability conditions and general solution for mixed Sylvester equations, Automatica, Volume 49 (2013), pp. 2713-2719

Cité par Sources :

Commentaires - Politique