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.
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@article{CRMATH_2015__353_11_1053_0, author = {Yuan, Yongxin}, 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}, url = {http://www.numdam.org/articles/10.1016/j.crma.2015.08.010/} }
TY - JOUR AU - Yuan, Yongxin 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 UR - http://www.numdam.org/articles/10.1016/j.crma.2015.08.010/ DO - 10.1016/j.crma.2015.08.010 LA - en ID - CRMATH_2015__353_11_1053_0 ER -
%0 Journal Article %A Yuan, Yongxin %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 %U http://www.numdam.org/articles/10.1016/j.crma.2015.08.010/ %R 10.1016/j.crma.2015.08.010 %G en %F CRMATH_2015__353_11_1053_0
Yuan, Yongxin. Solving the mixed Sylvester matrix equations by matrix decompositions. Comptes Rendus. Mathématique, Tome 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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