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 
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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/

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