Geodesic
An estimate of approximation of a matrix-valued function by an interpolation polynomial
Eurasian mathematical journal, Tome 11 (2020) no. 1, pp. 86-94.

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Let $A$ be a square complex matrix; $z_1,\dots,z_n\in\mathbb{C}$ be (possibly repetitive) points of interpolation; $f$ be a function analytic in a neighborhood of the convex hull of the union of the spectrum of $A$ and the points $z_1,\dots,z_n$; and $p$ be the interpolation polynomial of $f$ constructed by the points $z_1,\dots,z_n$. It is proved that under these assumptions $$ ||f(A)-p(A)||\leqslant \frac1{n!}\max_{t\in[0,1]\atop {\mu\in co\{z_1,z_2,\dots,z_n\}}}||\Omega(A)f^{(n)}((1-t)\mu\mathbf{1}+tA)||, $$ where $\Omega(z)=\prod_{k=1}^n(z-z_k)$ and the symbol $co$ means the convex hull. 
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V. G. Kurbatov; I. V. Kurbatova. An estimate of approximation of a matrix-valued function by an interpolation polynomial. Eurasian mathematical journal, Tome 11 (2020) no. 1, pp. 86-94. http://geodesic.mathdoc.fr/item/EMJ_2020_11_1_a6/

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