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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     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},
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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/

[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