Typical faces of best approximating polytopes with a restricted number of edges
Let K be a convex body in E3 with a C2 smooth boundary. In this article, we investigate polytopes with at most n edges circumscribed about K or inscribed in K, which approximate K best in the Hausdorff metric. The asymptotic behaviour of the distance, as a function of n, of such best approximating...
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2009
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| Sorozat: | Acta scientiarum mathematicarum
75 No. 1-2 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16304 |
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| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Vígh Viktor | |
| 245 | 1 | 0 | |a Typical faces of best approximating polytopes with a restricted number of edges |h [elektronikus dokumentum] / |c Vígh Viktor |
| 260 | |a Bolyai Institute, University of Szeged |b Szeged |c 2009 | ||
| 300 | |a 313-327 | ||
| 490 | 0 | |a Acta scientiarum mathematicarum |v 75 No. 1-2 | |
| 520 | 3 | |a Let K be a convex body in E3 with a C2 smooth boundary. In this article, we investigate polytopes with at most n edges circumscribed about K or inscribed in K, which approximate K best in the Hausdorff metric. The asymptotic behaviour of the distance, as a function of n, of such best approximating polytopes and K is known, see [3] for an asymptotic formula. In this article, we prove that the typical faces of the best approximating circumscribed or inscribed polytopes in the Hausdorff metric with at most n edges are asymptotically squares with respect to the second fundamental form of dK. | |
| 650 | 4 | |a Természettudományok | |
| 650 | 4 | |a Matematika | |
| 695 | |a Matematika | ||
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/16304/1/math_075_numb_001_002_313-327.pdf |z Dokumentum-elérés |