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- W2890470282 abstract "Recall that a convex body $K$ is in John's position if the unit Euclidean ball is the maximal volume ellipsoid contained in $K$. Approximating convex body in John's position by polytopes we obtain the following results. 1. Let $n>R_nge 1$ be a sequence such that $lim_{nrightarrow infty} frac{R_n}{n}=0$. For a sufficiently large $n$, we can construct a convex body $Ksubset mathbb{R}^n$ in John's position such that there is no $P$, polytope with a polynomial number of facets in $n$ such that $Ksubset Psubset R_nK$; 2. For a sufficiently large $n$, there is a convex body $Ksubset mathbb{R}^n$ in John's position such that there is no $P$, polytope that has less than $exp(cn)$ facets satisfies $Ksubset P subset sqrt{n}K$." @default.
- W2890470282 created "2018-09-27" @default.
- W2890470282 creator A5004151392 @default.
- W2890470282 date "2017-03-07" @default.
- W2890470282 modified "2023-09-27" @default.
- W2890470282 title "John's Position is not good for approximation." @default.
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