Approximation of the Euclidean ball by polytopes
Studia Mathematica, Tome 173 (2006) no. 1, pp. 1-18
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
There is a constant $c$ such that for every $n\in\mathbb N$,
there is an $N_{n}$ so that for
every $N\geq N_{n}$ there is a polytope $P_{}$ in $\mathbb R^{n}$
with $N$ vertices and
$$
\mathop{\rm vol}\nolimits _{n}(B_{2}^{n}\mathbin{\triangle} P)
\leq c \mathop{\rm vol}\nolimits _{n}(B_{2}^{n})N^{-\frac{2}{n-1}}
$$
where $B_{2}^{n}$ denotes the Euclidean unit ball of dimension $n$.
Keywords:
there constant every mathbb there every geq there polytope mathbb vertices mathop vol nolimits mathbin triangle leq mathop vol nolimits frac n where denotes euclidean unit ball dimension
Affiliations des auteurs :
Monika Ludwig 1 ; Carsten Schütt 2 ; Elisabeth Werner 3
@article{10_4064_sm173_1_1,
author = {Monika Ludwig and Carsten Sch\"utt and Elisabeth Werner},
title = {Approximation of the {Euclidean} ball by polytopes},
journal = {Studia Mathematica},
pages = {1--18},
publisher = {mathdoc},
volume = {173},
number = {1},
year = {2006},
doi = {10.4064/sm173-1-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm173-1-1/}
}
TY - JOUR AU - Monika Ludwig AU - Carsten Schütt AU - Elisabeth Werner TI - Approximation of the Euclidean ball by polytopes JO - Studia Mathematica PY - 2006 SP - 1 EP - 18 VL - 173 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm173-1-1/ DO - 10.4064/sm173-1-1 LA - en ID - 10_4064_sm173_1_1 ER -
Monika Ludwig; Carsten Schütt; Elisabeth Werner. Approximation of the Euclidean ball by polytopes. Studia Mathematica, Tome 173 (2006) no. 1, pp. 1-18. doi: 10.4064/sm173-1-1
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