Thomas Hangelbroek

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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. The main purpose of this paper is to study coordinate independent quadrature (or cubature) formulas associated with certain classes of positive definite and conditionally(More)
It is well-known that non-linear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for spline approximations and for wavelet approximations, and more recently for homogeneous radial basis function (surface(More)
The purpose of this article is to provide new error estimates for a popular type of SBF approximation on the sphere: approximating by linear combinations of Green’s functions of polyharmonic differential operators. We show that the Lp approximation order for this kind of approximation is σ for functions having Lp smoothness σ (for σ up to the order of the(More)
Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered data and is central to many meshless methods. For a set of N scattered sites, the standard basis for such a space utilizes N globally supported kernels; computing with it is(More)