I want to solve the following matrix equation. Could anyone give me a hand? Thanks.
Given an $n \times n$ matrix $\mathbf A$ (diagonally dominant), I need to solve an $n \times n$ symmetric matrix $\mathbf X$ such that
$\mathbf A\mathbf X+\mathbf X\mathbf A^\top =\mathbf I$,
where $\mathbf I$ is an $n \times n$ identity matrix.