64 citations · 228 across the 21 of their papers we have counts for
8 papers · 1 filter
Smoothing by, and eccentric smoothing of, compactly supported RBFs
Thomas Hangelbroek, Christian Rieger
We consider compactly supported RBFs having algebraically decaying Fourier transforms. Here we focus especially on generalized Wendland RBFs and their modification by making them s…
A Semi-Lagrangian scheme on embedded manifolds using generalized local polynomial reproductions
Thomas Hangelbroek, Christian Rieger, Grady B. Wright
We analyze rates of uniform convergence for a class of high-order semi-Lagrangian schemes for first-order, time-dependent partial differential equations on embedded submanifolds of…
Spectral stability and perturbation results for kernel differentiation matrices on the sphere
Thomas Hangelbroek, Christian Rieger, Grady Wright
We investigate the spectrum of differentiation matrices for certain operators on the sphere that are generated from collocation at a set of scattered points with positive defin…
Kernel Multi-Grid on Manifolds
Thomas Hangelbroek, Christian Rieger
Kernel methods for solving partial differential equations on surfaces have the advantage that those methods work intrinsically on the surface and yield high approximation rates if…
An inverse theorem for compact Lipschitz regions in using localized kernel bases
Thomas Hangelbroek, Francis J. Narcowich, Christian Rieger +1
While inverse estimates in the context of radial basis function approximation on boundary-free domains have been known for at least ten years, such theorems for the more important…
Direct and Inverse Results on Bounded Domains for Meshless Methods via Localized Bases on Manifolds
Thomas Hangelbroek, Francis J. Narcowich, Christian Rieger +1
This article develops direct and inverse estimates for certain finite dimensional spaces arising in kernel approximation. Both the direct and inverse estimates are based on approxi…
Kernel Based Quadrature on Spheres and Other Homogeneous Spaces
E. Fuselier, T. Hangelbroek, F. J. Narcowich +2
Quadrature formulas for spheres, the rotation group, and other compact, homogeneous manifolds are important in a number of applications and have been the subject of recent research…
Localized bases for kernel spaces on the unit sphere
E. Fuselier, T. Hangelbroek, F. J. Narcowich +2
Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered…