Geodesic
An analysis of the matrix equation $AX+\overline{X}B=C$
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 9, pp. 1556-1559

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The matrix equation $AX+\overline{X}B=C$, where $\overline{X}B$ is obtained by the entry-wise conjugation of $X$, is examined. On the basis of analogy with the Sylvester matrix equation, special cases are distinguished where the former equation corresponds to normal and self-adjoint Sylvester equations. Efficient numerical algorithms are proposed for these special cases. 
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     author = {Kh. D. Ikramov},
     title = {An analysis of the matrix equation $AX+\overline{X}B=C$},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1556--1559},
     publisher = {mathdoc},
     volume = {56},
     number = {9},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_9_a1/}
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Kh. D. Ikramov. An analysis of the matrix equation $AX+\overline{X}B=C$. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 9, pp. 1556-1559. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_9_a1/