Geodesic
Modifying a numerical algorithm for solving the matrix equation $X+AX^TB=C$
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 6, pp. 853-856 
Yu. O. Vorontsov. Modifying a numerical algorithm for solving the matrix equation $X+AX^TB=C$. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 6, pp. 853-856. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_6_a1/
@article{ZVMMF_2013_53_6_a1,
     author = {Yu. O. Vorontsov},
     title = {Modifying a numerical algorithm for solving the matrix equation $X+AX^TB=C$},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {853--856},
     year = {2013},
     volume = {53},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_6_a1/}
}
TY  - JOUR
AU  - Yu. O. Vorontsov
TI  - Modifying a numerical algorithm for solving the matrix equation $X+AX^TB=C$
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2013
SP  - 853
EP  - 856
VL  - 53
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_6_a1/
LA  - ru
ID  - ZVMMF_2013_53_6_a1
ER  - 
%0 Journal Article
%A Yu. O. Vorontsov
%T Modifying a numerical algorithm for solving the matrix equation $X+AX^TB=C$
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2013
%P 853-856
%V 53
%N 6
%U http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_6_a1/
%G ru
%F ZVMMF_2013_53_6_a1

Voir la notice de l'article provenant de la source Math-Net.Ru

Certain modifications are proposed for a numerical algorithm solving the matrix equation $X+AX^TB=C$. By keeping the intermediate results in storage and repeatedly using them, it is possible to reduce the total complexity of the algorithm from $O(n^4)$ to $O(n^3)$ arithmetic operations.

[1] Zhou V., Lam J., Duan C.-R., “Toward solution of matrix equation $X=Af(X)B+C$”, Linear Algebra Appl., 435:11 (2011), 1370–1398 | DOI | MR | Zbl

[2] Ikramov Kh. D., Vorontsov Yu. O., “Matrichnoe uravnenie $X+AX^{\mathrm T}B=C$: usloviya odnoznachnoi razreshimosti i algoritm chislennogo resheniya”, Dokl. AN, 443:5 (2012), 545–548 | MR | Zbl