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Approximation de convexes par des polytopes et décomposition approchée de normes

Abstract : Approximating smooth convex by polytopes with respect to Hausdorff metric is a field where numerous results were recently obtained thanks to the riemannian geometry. We first recall these results, essentialy focused on the asymtotic behaviour, and show their utility for some special cases. We then prove our main result stating that approximating a convex is somewhat equivalent to approximating a norm. We establish several properties of the product of norm approximations, so that we can construct, by recurrence over the dimension, good approximating polytopes for specific convexes, as well as optimal approximating norms for some norms like the Lp ones. We finish by showing some applications in the field of computational geometry. An approximation of the norm can indeed transform an exact algorithm into a faster algorithm that gives an approximate solution.
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https://tel.archives-ouvertes.fr/tel-00005258
Contributor : François Gannaz <>
Submitted on : Tuesday, March 9, 2004 - 9:51:27 AM
Last modification on : Friday, November 6, 2020 - 4:04:29 AM
Long-term archiving on: : Wednesday, September 12, 2012 - 2:00:16 PM

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  • HAL Id : tel-00005258, version 1

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François Gannaz. Approximation de convexes par des polytopes et décomposition approchée de normes. Modélisation et simulation. Université Joseph-Fourier - Grenoble I, 2003. Français. ⟨tel-00005258⟩

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