Numerical analysis
Solving the mixed Sylvester matrix equations by matrix decompositions
Comptes Rendus. Mathématique, Volume 353 (2015) no. 11, pp. 1053-1059.

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.

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.

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DOI: 10.1016/j.crma.2015.08.010
Yuan, Yongxin 1

1 School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, PR China
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Yuan, Yongxin. 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. http://www.numdam.org/articles/10.1016/j.crma.2015.08.010/

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