  Let $A$ be a square complex matrix, $z_1$, ..., $z_{n}\in\mathbb C$ be
(possibly repetitive) points of interpolation, $f$ be analytic in a
neighborhood of the convex hull of the union of the spectrum of $A$ and the
points $z_1$, ..., $z_{n}$, and $p$ be the interpolation polynomial of $f$,
constructed by the points $z_1$, ..., $z_{n}$. It is proved that under these
assumptions $$\Vert f(A)-p(A)\Vert\le\frac1{n!}
\max_{t\in[0,1];\,\mu\in\text{co}\{z_1,z_{2},\dots,z_{n}\}}\bigl\Vert\Omega(A)f^{{(n)}}
\bigl((1-t)\mu\mathbf1+tA\bigr)\bigr\Vert,$$ where
$\Omega(z)=\prod_{k=1}^n(z-z_k)$.
