Geodesic
Numerical solution of matrix equations of the Stein type in the self-adjoint case
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 5, pp. 723-727 
Yu. O. Vorontsov; Kh. D. Ikramov. Numerical solution of matrix equations of the Stein type in the self-adjoint case. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 5, pp. 723-727. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_5_a0/
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     title = {Numerical solution of matrix equations of the {Stein} type in the self-adjoint case},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The algorithms for solving the equations $X-AX^TB=C$ and $X-AX^*B=C$ proposed by the authors in earlier publications are now modified for the case where these equations can be regarded as self-adjoint ones. 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

[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

[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

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

[6] Vorontsov Yu. O., Ikramov Kh. D., “O chislennom reshenii matrichnykh uravnenii $AX+X^TB=C$ i $X+AX^TB=C$ s pryamougolnymi koeffitsientami $A$ i $B$”, Zap. nauchn. semin. POMI, 405, 2012, 54–58 | MR