Spherical $t_\epsilon $-designs for approximations on the sphere
From MaRDI portal
Publication:3177718
DOI10.1090/mcom/3306OpenAlexW2963976101MaRDI QIDQ3177718
Publication date: 1 August 2018
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1502.03562
numerical integrationpolynomial approximationinterval analysisspherical \(t\)-designs\(l_1\)-regularization
Interval and finite arithmetic (65G30) Approximation by polynomials (41A10) Numerical integration (65D30)
Related Items
Efficient Spherical Designs with Good Geometric Properties, Continuous regularized least squares polynomial approximation on the sphere, Quadrature rules with neighborhood of spherical designs on the two-sphere, Enclosing Chebyshev Expansions in Linear Time, Spherical half-designs of high order
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A smoothing trust region filter algorithm for nonsmooth least squares problems
- Optimal asymptotic bounds for spherical designs
- A characterization of Sobolev spaces on the sphere and an extension of Stolarsky's invariance principle to arbitrary smoothness
- Computational existence proofs for spherical \(t\)-designs
- On the computation of spherical designs by a new optimization approach based on fast spherical Fourier transforms
- Spherical harmonics and approximations on the unit sphere. An introduction
- Filtered hyperinterpolation: a constructive polynomial approximation on the sphere
- Numerical integration over spheres of arbitrary dimension
- A variational characterisation of spherical designs
- A survey on spherical designs and algebraic combinatorics on spheres
- Averaging sets: A generalization of mean values and spherical designs
- Construction of spherical \(t\)-designs
- Spherical codes and designs
- Distributing many points on a sphere
- McLaren's improved snub cube and other new spherical designs in three dimensions
- Cubature over the sphere \(S^{2}\) in Sobolev spaces of arbitrary order
- Remarks on the concepts of \(t\)-designs
- Spherical harmonics
- A simple proof of Stolarsky’s invariance principle
- Regularized Least Squares Approximations on the Sphere Using Spherical Designs
- Well Conditioned Spherical Designs for Integration and Interpolation on the Two-Sphere
- QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere
- Multivariate interpolation of large sets of scattered data
- Spherical Designs, Discrepancy and Numerical Integration
- Quadrature Rules for the Surface Integral of the Unit Sphere Based on Extremal Fundamental Systems
- Worst-case errors in a Sobolev space setting for cubature over the sphere S2
- Spherical faraday cage for the case of equal point charges and chebyshev-type quadrature on the sphere
- Parameter Choice Strategies for Least-squares Approximation of Noisy Smooth Functions on the Sphere
- Existence of Solutions to Systems of Underdetermined Equations and Spherical Designs
- Scattered Data Approximation
- On tight spherical designs
