Polytope Approximation and the Mahler Volume (Preprint)
HONG KONG UNIV OF SCIENCE AND TECHNOLOGY KOWLOON
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The problem of approximating convex bodies by polytopes is an important and well studied problem. Given a convex body K in Rd, the objective is to minimize the number of vertices alternatively, the number of facets of an approximating polytope for a given Hausdorff error epsilon. Results to date have been of two types. The first type assumes that K is smooth, and bounds hold in the limit as epsilon tends to zero. The second type requires no such assumptions. The latter type includes the well known results of Dudley 1974 and Bronshteyn and Ivanov 1976, which show that in spaces of fixed dimension, OdiamKepsilond-12 vertices alt., facets suffice. Our results are of this latter type.
- Numerical Mathematics