Geodesic
Best methods of interpolation for certain classes of differentiable functions
Matematičeskie zametki, Tome 17 (1975) no. 4, pp. 511-524.

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For the class $W^{(r)}L_q(M;a,b)$, $1\le q\le\infty$, we construct the best method of approximation of the functional $f(x)$, $x\in[a,b]$, among all the methods using only information about the values of $f^{(k)}(k=0,1,\dots,r-1;i=1,2,\dots,N)$. 
@article{MZM_1975_17_4_a2,
     author = {B. D. Boyanov},
     title = {Best methods of interpolation for certain classes of differentiable functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {511--524},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_4_a2/}
}
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B. D. Boyanov. Best methods of interpolation for certain classes of differentiable functions. Matematičeskie zametki, Tome 17 (1975) no. 4, pp. 511-524. http://geodesic.mathdoc.fr/item/MZM_1975_17_4_a2/