Geodesic
Orthogonal projection and minimal linear interpolation on a $n$-dimensional cube
Modelirovanie i analiz informacionnyh sistem, Tome 14 (2007) no. 3, pp. 8-28 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $H$ be the orthogonal projection onto polynomials of $n$ variables of degree $\le 1$ and $\|\cdot\|$ be the norm of an operator from $C([0,1]^n)$ to $C([0,1]^n)$. In this paper we show that $C_1\theta_n\le\|H\|\le C_2\theta_n$, $n\in\mathrm{N}$. Here $\theta_n$ denotes the minimal norm of a projection dealing with the linear interpolation on the cube $[0,1]^n$. The proofs make use of certain properties of the Eulerian numbers and the central $B$-splines and also some previous results of the author. 
@article{MAIS_2007_14_3_a1,
     author = {M. V. Nevskij},
     title = {Orthogonal projection and minimal linear interpolation on a $n$-dimensional cube},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {8--28},
     year = {2007},
     volume = {14},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2007_14_3_a1/}
}
TY  - JOUR
AU  - M. V. Nevskij
TI  - Orthogonal projection and minimal linear interpolation on a $n$-dimensional cube
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2007
SP  - 8
EP  - 28
VL  - 14
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MAIS_2007_14_3_a1/
LA  - ru
ID  - MAIS_2007_14_3_a1
ER  - 
%0 Journal Article
%A M. V. Nevskij
%T Orthogonal projection and minimal linear interpolation on a $n$-dimensional cube
%J Modelirovanie i analiz informacionnyh sistem
%D 2007
%P 8-28
%V 14
%N 3
%U http://geodesic.mathdoc.fr/item/MAIS_2007_14_3_a1/
%G ru
%F MAIS_2007_14_3_a1
M. V. Nevskij. Orthogonal projection and minimal linear interpolation on a $n$-dimensional cube. Modelirovanie i analiz informacionnyh sistem, Tome 14 (2007) no. 3, pp. 8-28. http://geodesic.mathdoc.fr/item/MAIS_2007_14_3_a1/

[1] M. V. Nevskii, “Geometricheskie metody v zadache o minimalnom proektore”, Modelipovanie i analiz infopmatsionnykh sistem, 13:2 (2006), 16–29

[2] M. V. Nevskii, “Minimalnye proektory i maksimalnye simpleksy”, Modelipovanie i analiz infopmatsionnykh sistem, 14:1 (2007), 3–10

[3] P. L. Butzer, M. Schmidt, E. L. Stark, “Observations on the history of central B-splines”, Archive for History of Exact Sciences, 39:2 (1988), 137–156 | MR | Zbl

[4] L. Comtet, “Permutations by number of rises; Eulerian numbers”, Advanced Combinatorics: The Art of Finite and Infinite Expansions, 1974, 240–246, Reidel, Dordrecht, Netherlands

[5] R. Ehrenborg, M. Readdy, E. Steingrimsson, “Mixed volumes and slices of the cube”, Journal of Combinatorial Theory, Series A, 81 (1998), 121–126 | DOI | Zbl