AbstractIt is well known that the equation {x^{\prime}(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 formx(t)=\int_{-\infty}^{\infty}\mathcal{G}(t-s)f(s)\,ds.The kernel {\mathcal{G}} is called Green’s function. In this paper, for approximate calculation of {\mathcal{G}}, the Newton interpolating polynomial of a special function {g_{t}} is used. An estimate of the sensitivity of the problem is given. The results of numerical experiments are presented.
On the Fekete–Szegö type functionals for functions which are convex in the direction of the imaginary axis
