Abstract:
A relationship is found between the solutions to the sesquilinear matrix equation $X^*DX+AX+X^*B+C=0$, where all the matrix coefficients are $n\times n$ matrices, and the neutral subspaces of the $2n\times 2n$ matrix $M=\begin{pmatrix}C& A\\ B& D\end{pmatrix}$. 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.
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