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 
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/
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     title = {Numerical solution of matrix equations of the form $X+AX^{\mathrm T}B=C$},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[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