  It is well known that the equation $x'(t)=Ax(t)+f(t)$, where $A$ is a square
matrix, has a unique bounded solution $x$ for any bounded continuous free term
$f$, provided the coefficient $A$ has no eigenvalues on the imaginary axis.
This solution can be represented in the form \begin{equation*}
x(t)=\int_{-\infty}^{\infty}\mathcal G(t-s)x(s)\,ds. \end{equation*} The kernel
$\mathcal G$ is called Green's function. In the paper, a representation of
Green's function in the form of the Newton interpolating polynomial is used for
approximate calculation of $\mathcal G$. An estimate of the sensitivity of the
problem is given.
