Geodesic
Numerical solution of the discrete BHH-equation in the normal case
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 21 (2018) no. 4, pp. 367-373

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It is known that the solution of the semilinear matrix equation $X-A\overline XB=C$ can be reduced to solving the classical Stein equation. The normal case means that the coefficients on the left-hand side of the resulting equation are normal matrices. We propose a method for solving the original semilinear equation in the normal case that permits to almost halve the execution time for equations of order $n=3000$ compared to the library function dlyap, which solves Stein equations in Matlab. 
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     author = {Kh. D. Ikramov and Yu. O. Vorontsov},
     title = {Numerical solution of the discrete {BHH-equation} in the normal case},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {367--373},
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     year = {2018},
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Kh. D. Ikramov; Yu. O. Vorontsov. Numerical solution of the discrete BHH-equation in the normal case. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 21 (2018) no. 4, pp. 367-373. http://geodesic.mathdoc.fr/item/SJVM_2018_21_4_a1/