Numerical algorithm for solving quadratic matrix equations of a certain class

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 $M=\begin{pmatrix}C&A\\B&D\end{pmatrix}$. 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.