Comptes Rendus
no. 19-20
Optimal Control/Numerical Analysis
On solutions of the matrix equations KX−EXF=BY and MXF2+DXF+KX=BY
[Sur les solutions des équations matricielles KX−EXF=BY et MXF2+DXF+KX=BY]

Présenté par : Olivier Pironneau

Yongxin Yuan1 ; Jiashang Jiang1
1 School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang 212003, PR China
Comptes Rendus. Mathématique, Volume 350 (2012) no. 19-20, pp. 903-906.

Dans cette note on étudie les solutions des équations généralisées de Sylvester KX−EXF=BY et MFX2+DXF+KX=BY, on donne des expressions explicites des solutions de ces équations en utilisant des transformations matricielles et le polynôme minimal de la matrice F.

This note studies the solutions of generalized Sylvester equations KX−EXF=BY and MXF2+DXF+KX=BY, and obtains explicit solutions of the equations by using some matrix transformations and the minimal polynomial of the matrix F.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.10.011

Yongxin Yuan 1 ; Jiashang Jiang 1

1 School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang 212003, PR China 
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Yongxin Yuan; Jiashang Jiang. On solutions of the matrix equations $ KX-EXF=BY$ and $ MX{F}^{2}+DXF+KX=BY$. Comptes Rendus. Mathématique, Volume 350 (2012) no. 19-20, pp. 903-906. doi : 10.1016/j.crma.2012.10.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.10.011/

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  • Masoud Hajarian Convergence properties of BCR method for generalized Sylvester matrix equation over generalized reflexive and anti-reflexive matrices, Linear and Multilinear Algebra, Volume 66 (2018) no. 10, p. 1975 | DOI:10.1080/03081087.2017.1382441
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