Cubature over the sphere \(S^{2}\) in Sobolev spaces of arbitrary order
From MaRDI portal
Publication:2502871
DOI10.1016/j.jat.2006.01.004zbMath1102.41027OpenAlexW2047342172MaRDI QIDQ2502871
Publication date: 13 September 2006
Published in: Journal of Approximation Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jat.2006.01.004
Related Items (30)
An optimal cascadic multigrid method for the radiative transfer equation ⋮ Analysis of a full discretization scheme for \(2D\) radiative-conductive heat transfer systems ⋮ Spherical $t_\epsilon $-designs for approximations on the sphere ⋮ An octahedral equal area partition of the sphere and near optimal configurations of points ⋮ QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere ⋮ Distributed learning via filtered hyperinterpolation on manifolds ⋮ A component-by-component approach to efficient numerical integration over products of spheres ⋮ Reduced Order Observer of Finite Dimensional Radiative-Conductive Heat Transfer Systems ⋮ A characterization of Sobolev spaces on the sphere and an extension of Stolarsky's invariance principle to arbitrary smoothness ⋮ Spherical basis functions and uniform distribution of points on spheres ⋮ Bypassing the quadrature exactness assumption of hyperinterpolation on the sphere ⋮ Explicit Families of Functions on the Sphere with Exactly Known Sobolev Space Smoothness ⋮ Efficient Spherical Designs with Good Geometric Properties ⋮ Hyperuniform point sets on flat tori: deterministic and probabilistic aspects ⋮ Discrepancy and numerical integration on metric measure spaces ⋮ The Coulomb energy of spherical designs on \(S^{2}\) ⋮ Inequalities for zeros of Jacobi polynomials via Sturm's theorem: Gautschi's conjectures ⋮ Positive weight quadrature on the sphere and monotonicities of Jacobi polynomials ⋮ Quadrature in Besov spaces on the Euclidean sphere ⋮ Needlet approximation for isotropic random fields on the sphere ⋮ Upper and lower estimates for numerical integration errors on spheres of arbitrary dimension ⋮ Optimal logarithmic energy points on the unit sphere ⋮ Complexity of numerical integration over spherical caps in a Sobolev space setting ⋮ A lower bound for the worst-case cubature error on spheres of arbitrary dimension ⋮ OPTIMAL LOWER ESTIMATES FOR THE WORST CASE CUBATURE ERROR AND THE APPROXIMATION BY HYPERINTERPOLATION OPERATORS IN THE SOBOLEV SPACE SETTING ON THE SPHERE ⋮ The \(s\)-energy of spherical designs on \(S^{2}\) ⋮ Sampling, Marcinkiewicz-Zygmund inequalities, approximation, and quadrature rules ⋮ Optimal lower bounds for cubature error on the sphere \(S^2\) ⋮ Numerical nonlinear complex geometrical optics algorithm for the 3D Calderón problem ⋮ Distributing many points on spheres: minimal energy and designs
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Hyperinterpolation on the sphere at the minimal projection order
- Kolmogorov width of classes of smooth functions on the sphere \(\mathbb S^{d-1}\)
- Constructive polynomial approximation on the sphere
- Spherical harmonics
- Optimal lower bounds for cubature error on the sphere \(S^2\)
- Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature
- Approximation by Ridge Functions and Neural Networks
- Worst-case errors in a Sobolev space setting for cubature over the sphere S2
This page was built for publication: Cubature over the sphere \(S^{2}\) in Sobolev spaces of arbitrary order
