Curve based approximation of measures on manifolds by discrepancy minimization
From MaRDI portal
Publication:2067682
DOI10.1007/s10208-021-09491-2zbMath1491.65048arXiv1910.06124OpenAlexW2980049123MaRDI QIDQ2067682
Manuel Gräf, Sebastian Neumayer, Martin Ehler, Gabriele Drauschke
Publication date: 18 January 2022
Published in: Foundations of Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1910.06124
manifoldscurvessampling theorynon-convex optimizationquadrature rulesFourier methodsapproximation of measures
Nonconvex programming, global optimization (90C26) Numerical optimization and variational techniques (65K10)
Related Items (4)
Approximation properties of the double Fourier sphere method ⋮ t-Design Curves and Mobile Sampling on the Sphere ⋮ Mathematical imaging and surface processing. Abstracts from the workshop held August 21--27, 2022 ⋮ Unbalanced multi-marginal optimal transport
Uses Software
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
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Computational Optimal Transport: With Applications to Data Science
- Optimal asymptotic bounds for spherical designs
- Mercer's theorem on general domains: on the interaction between measures, kernels, and RKHSs
- A projection method on measures sets
- Diameter bounded equal measure partitions of Ahlfors regular metric measure spaces
- Marcinkiewicz-Zygmund measures on manifolds
- On the computation of spherical designs by a new optimization approach based on fast spherical Fourier transforms
- Weighted geometric discrepancies and numerical integration on reproducing kernel Hilbert spaces
- A unified approach to scattered data approximation on \(\mathbb{S}^{\mathbf {3}}\) and \(\mathrm{SO(3)}\)
- On minimal trajectories for mobile sampling of bandlimited fields
- Tractability of multivariate problems. Volume II: Standard information for functionals.
- Eignets for function approximation on manifolds
- Growth rates of Euclidean minimal spanning trees with power weighted edges
- On means of distances on the surface of a sphere. II: Upper bounds
- Extremal properties of principal curves in the plane
- Codes and designs in Grassmannian spaces.
- Differentiation and regularity of semi-discrete optimal transport with respect to the parameters of the discrete measure
- Reproducing kernels for the irreducible components of polynomial spaces on unions of Grassmannians
- Numerical Fourier analysis
- Designs in Grassmannian spaces and lattices
- Well-separated spherical designs
- Bounds for codes and designs in complex subspaces
- Quadrature in Besov spaces on the Euclidean sphere
- Spherical harmonics
- On averaging sets
- Sobolev algebras on Lie groups and Riemannian manifolds
- On the mathematical foundations of learning
- Consistency of variational continuous-domain quantization via kinetic theory
- Scattered Data Interpolation on Embedded Submanifolds with Restricted Positive Definite Kernels: Sobolev Error Estimates
- Optimization Methods on Riemannian Manifolds and Their Application to Shape Space
- Approximation by finitely supported measures
- Using NFFT 3---A Software Library for Various Nonequispaced Fast Fourier Transforms
- Dithering by Differences of Convex Functions
- Sampling Sets and Quadrature Formulae on the Rotation Group
- The Grand Tour: A Tool for Viewing Multidimensional Data
- On Estimates for the Weights in Gaussian Quadrature in the Ultraspherical Case
- Linear programming bounds for codes in grassmannian spaces
- Worst-Case Growth Rates of Some Classical Problems of Combinatorial Optimization
- Optimization Techniques on Riemannian Manifolds
- Quasi Monte Carlo Integration and Kernel-Based Function Approximation on Grassmannians
- Uniform decomposition of probability measures: quantization, clustering and rate of convergence
- Approximate Quadrature Measures on Data-Defined Spaces
- Principal Curves
- Generalized Jacobi Polynomials as Spherical Functions of the Grassmann Manifold
- Quadrature Errors, Discrepancies, and Their Relations to Halftoning on the Torus and the Sphere
- Variable Density Sampling with Continuous Trajectories
- Quadrature rules and distribution of points on manifolds
- On the Generation of Sampling Schemes for Magnetic Resonance Imaging
- The Conjugate Gradient Method for Linear and Nonlinear Operator Equations
- Optimal Transport Approximation of 2-Dimensional Measures
This page was built for publication: Curve based approximation of measures on manifolds by discrepancy minimization
