7 papers
Adaptive RBF-multiscale approximation on bounded domains
Federico Lot, Christian Rieger
This article addresses adaptivity in the kernel multiscale method. Adaptively compressed kernel multiscale approximations have already been presented and analyzed in (LeGia & Wendl…
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…
Kernel approximation beyond the native space -- with applications to approximation on manifolds
Thomas Hangelbroek, Christian Rieger, Grady B. Wright
This article treats kernel approximation and interpolation on embedded manifolds of using restrictions of positive and conditionally positive definite kernels. The ma…
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…
Efficiently parallelizable kernel-based multi-scale algorithm
Federico Lot, Christian Rieger
The kernel-based multi-scale method has been proven to be a powerful approximation method for scattered data approximation problems which is computationally superior to conventiona…
Generalized local polynomial reproductions
Thomas Hangelbroek, Christian Rieger, Grady B. Wright
We present a general framework, treating Lipschitz domains in Riemannian manifolds, that provides conditions guaranteeing the existence of norming sets and generalized local polyno…
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…