Points on manifolds with asymptotically optimal covering radius
From MaRDI portal
Publication:722761
DOI10.1016/j.jco.2018.03.002OpenAlexW3102893798MaRDI QIDQ722761
Manuel Gräf, Anna Breger, Martin Ehler
Publication date: 27 July 2018
Published in: Journal of Complexity (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1607.06899
Riemannian manifoldCovering radiusCubature pointsQuasi-Monte Carlo integrationWorst case integration error
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Cites Work
- Unnamed Item
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- Unnamed Item
- Optimal asymptotic bounds for spherical designs
- Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces
- Marcinkiewicz-Zygmund measures on manifolds
- Tractability of multivariate problems. Volume II: Standard information for functionals.
- Averaging sets: A generalization of mean values and spherical designs
- Spherical functions on the Grassmann manifold and generalized Jacobi polynomials. 2
- Energy functionals, numerical integration and asymptotic equidistribution on the sphere.
- Some current issues in quasi-Monte Carlo methods
- Codes and designs in Grassmannian spaces.
- Extremal systems of points and numerical integration on the sphere
- Asymptotically optimal designs on compact algebraic manifolds
- Designs in Grassmannian spaces and lattices
- Statistics on special manifolds
- Numerical properties of generalized discrepancies on spheres of arbitrary dimension
- A quadrature formula for diffusion polynomials corresponding to a generalized heat kernel
- Tight \(p\)-fusion frames
- Distributing many points on spheres: minimal energy and designs
- Designs, groups and lattices
- Optimal cubature in Besov spaces with dominating mixed smoothness on the unit square
- The curse of dimensionality for numerical integration of smooth functions. II
- QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere
- Quasi Monte Carlo Integration and Kernel-Based Function Approximation on Grassmannians
- Quadrature rules and distribution of points on manifolds
- Lower bounds for the integration error for multivariate functions with mixed smoothness and optimal Fibonacci cubature for functions on the square
- Open type quasi-Monte Carlo integration based on Halton sequences in weighted Sobolev spaces
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