Best and random approximation of a convex body by a polytope
From MaRDI portal
Publication:2136855
DOI10.1016/j.jco.2022.101652zbMath1489.52009arXiv2111.07306OpenAlexW4213220871WikidataQ114163586 ScholiaQ114163586MaRDI QIDQ2136855
Joscha Prochno, Elisabeth M. Werner, Carsten Schuett
Publication date: 16 May 2022
Published in: Journal of Complexity (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2111.07306
polytopeconvex bodybest approximationfloating bodyaffine surface arearandom approximationvolume difference
Geometric probability and stochastic geometry (60D05) Approximation by convex sets (52A27) Random convex sets and integral geometry (aspects of convex geometry) (52A22)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A Mathematical Theory of Communication
- Approaching the Kannan-Lovász-Simonovits and variance conjectures
- Hastings's additivity counterexample via Dvoretzky's theorem
- Equivalence of additivity questions in quantum information theory
- Expectation of intrinsic volumes of random polytopes
- Volume approximation of convex bodies by inscribed polytopes
- Diameter of the Minkowski compactum is approximately equal to n
- The convex floating body and polyhedral approximation
- Ellipsoids of maximal volume in convex bodies
- Polygonal approximation of plane convex bodies
- Random polytopes in a convex polytope, independence of shape, and concentration of vertices
- On affine plane curve evolution
- Umbrellas and polytopal approximation of the Euclidean ball
- The surface area deviation of the Euclidean ball and a polytope
- Approximation of smooth convex bodies by random polytopes
- Approximation of a ball by random polytopes
- On the mean value of the volume of a random polytope in a convex set
- Constructing a polytope to approximate a convex body
- A characterization of affine length and asymptotic approximation of convex discs
- Polytopal approximation bounding the number of \(k\)-faces
- Surface area deviation between smooth convex bodies and polytopes
- Function values are enough for \(L_2\)-approximation
- Metric entropy of some classes of sets with differentiable boundaries
- On the convex hull of uniform random points in a simple \(d\)-polytope
- On some mean values associated with a randomly selected simplex in a convex set
- Dropping a vertex or a facet from a convex polytope
- Random points on the boundary of smooth convex bodies
- Graph Theory and Probability
- Graph Theory and Probability. II
- 4. On the power of random information
- Convex bodies, economic cap coverings, random polytopes
- Approximation of Convex Bodies by Polytopes
- The convex floating body.
- On the mean value of the area of a random polygon in a plane convex body
- Random polytopes in a convex body
- Asymptotic estimates for best and stepwise approximation of convex bodies II
- Random Polytopes and Affine Surface Area
- Asymptotic approximation of smooth convex bodies by general polytopes
- Randomized algorithms in numerical linear algebra
- Random sections of ellipsoids and the power of random information
- Nonadditivity of Rényi entropy and Dvoretzky’s theorem
- Convex and Discrete Geometry
- [https://portal.mardi4nfdi.de/wiki/Publication:5331598 �ber die konvexe H�lle von n zuf�llig gew�hlten Punkten. II]
- Approximation of the Euclidean ball by polytopes
- [https://portal.mardi4nfdi.de/wiki/Publication:5728818 �ber die konvexe H�lle von n zuf�llig gew�hlten Punkten]
- A Lower Bound for the Volume of Strictly Convex Bodies with many Boundary Lattice Points
- A simple proof of an estimate for the approximation of the Euclidean ball and the Delone triangulation numbers
- On the Delone triangulation numbers