Geodesic
Numerical algorithm for solving quadratic matrix equations of a certain class
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 11, pp. 1707-1710

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A relationship is found between the solutions to the quadratic matrix equation $X^TDX+AX+X^TB+C=0$, where all the matrix coefficients are $n\times n$ matrices, and the neutral subspaces of the $2n\times 2n$ matrix $2n\times 2n$-матрицы $M=\begin{pmatrix}C\\B\end{pmatrix}$. This relationship is used to design an algorithm for solving matrix equations of the indicated type. Numerical results obtained with the help of the proposed algorithm are presented. 
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     author = {Yu. O. Vorontsov and Kh. D. Ikramov},
     title = {Numerical algorithm for solving quadratic matrix equations of a certain class},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     number = {11},
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Yu. O. Vorontsov; Kh. D. Ikramov. Numerical algorithm for solving quadratic matrix equations of a certain class. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 11, pp. 1707-1710. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_11_a1/