Geodesic
Numerical solution of the matrix equation $X-A\overline{X}B=C$ in the self-adjoint case
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 3, pp. 371-374 
Yu. O. Vorontsov; Kh. D. Ikramov. Numerical solution of the matrix equation $X-A\overline{X}B=C$ in the self-adjoint case. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 3, pp. 371-374. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_3_a0/
@article{ZVMMF_2014_54_3_a0,
     author = {Yu. O. Vorontsov and Kh. D. Ikramov},
     title = {Numerical solution of the matrix equation $X-A\overline{X}B=C$ in the self-adjoint case},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {371--374},
     year = {2014},
     volume = {54},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_3_a0/}
}
TY  - JOUR
AU  - Yu. O. Vorontsov
AU  - Kh. D. Ikramov
TI  - Numerical solution of the matrix equation $X-A\overline{X}B=C$ in the self-adjoint case
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2014
SP  - 371
EP  - 374
VL  - 54
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_3_a0/
LA  - ru
ID  - ZVMMF_2014_54_3_a0
ER  - 
%0 Journal Article
%A Yu. O. Vorontsov
%A Kh. D. Ikramov
%T Numerical solution of the matrix equation $X-A\overline{X}B=C$ in the self-adjoint case
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2014
%P 371-374
%V 54
%N 3
%U http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_3_a0/
%G ru
%F ZVMMF_2014_54_3_a0

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

The numerical algorithm for solving the equation $X-A\overline{X}B=C$ proposed in an earlier publication is now modified for the situation where this equation can be regarded as a self-adjoint one. The economy in the computational time and work achieved through these modifications is illustrated by numerical results.

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

[2] Vorontsov Yu. O., Ikramov Kh. D., “Chislennoe reshenie matrichnykh uravnenii vida $X+AX^TB=C$”, Zh. vychisl. matem. i matem. fiz., 53:3 (2013), 331–335 | DOI | Zbl

[3] Vorontsov Yu. O., “Modifikatsiya chislennogo algoritma dlya resheniya matrichnogo uravneniya $X+AX^TB=C$”, Zh. vychisl. matem. i matem. fiz., 53:6 (2013), 853–856 | DOI

[4] 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

[5] Ikramov Kh. D., Vorontsov Yu. O., “Chislennoe reshenie matrichnykh uravnenii Silvestra v samosopryazhennom sluchae”, Vestn. MGU, 2014, no. 2 | MR

[6] Vorontsov Yu. O., Ikramov Kh. D., “Chislennoe reshenie matrichnykh uravnenii tipa Steina v samosopryazhennom sluchae”, Zh. vychisl. matem. i matem. fiz., 54:2 (2014) | MR

[7] Ikramov Kh. D., “Usloviya samosopryazhennosti matrichnykh uravnenii tipa Steina”, Dokl. AN, 451:5 (2013), 498–500 | DOI | MR | Zbl

[8] Khorn R., Dzhonson Ch., Matrichnyi analiz, Mir, M., 1989 | MR