Geodesic
Numerical solution of matrix equations of the form $X+AX^{\mathrm T}B=C$
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 3, pp. 331-335 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A review of numerical methods for solving matrix equations of the form $X+AX^{\mathrm T}B=C$ is given. The methods under consideration were implemented in the Matlab environment. The performances of these methods are compared, including the case where the conditions for unique solvability are “almost” violated. 
@article{ZVMMF_2013_53_3_a0,
     author = {Yu. O. Vorontsov and Khakim D. Ikramov},
     title = {Numerical solution of matrix equations of the form $X+AX^{\mathrm T}B=C$},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {331--335},
     year = {2013},
     volume = {53},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_3_a0/}
}
TY  - JOUR
AU  - Yu. O. Vorontsov
AU  - Khakim D. Ikramov
TI  - Numerical solution of matrix equations of the form $X+AX^{\mathrm T}B=C$
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2013
SP  - 331
EP  - 335
VL  - 53
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_3_a0/
LA  - ru
ID  - ZVMMF_2013_53_3_a0
ER  - 
%0 Journal Article
%A Yu. O. Vorontsov
%A Khakim D. Ikramov
%T Numerical solution of matrix equations of the form $X+AX^{\mathrm T}B=C$
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2013
%P 331-335
%V 53
%N 3
%U http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_3_a0/
%G ru
%F ZVMMF_2013_53_3_a0
Yu. O. Vorontsov; Khakim D. Ikramov. Numerical solution of matrix equations of the form $X+AX^{\mathrm T}B=C$. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 3, pp. 331-335. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_3_a0/

[1] Gantmakher F. R., Teoriya matrits, Nauka, M., 1966 | MR

[2] Ikramov Kh. D., Chislennoe reshenie matrichnykh uravnenii, Nauka, M., 1984 | MR | Zbl

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

[4] Ikramov Kh. D., Vorontsov Yu. O., “Matrichnoe uravnenie $X+AX^{\mathrm T}B=C$: usloviya odnoznachnoi razreshimosti i algoritm chislennogo resheniya”, Dokl. AN, 433:5 (2012), 545–548 | MR