9 papers
Optimal compression of kernel matrices by interpolets with application to high-dimensional approximation
Helmut Harbrecht, Lucio Antonio Rosi
We consider the compression of kernel matrices on the unit interval by interpolets that have sufficiently many vanishing moments. We define a compression rule which discard…
Simulation of Gaussian random fields on surfaces using the isogeometric finite element method
Helmut Harbrecht, Florian Sonderegger, Remo von Rickenbach
We are concerned with the fast simulation of random fields on closed surfaces in which are generated by the (Whittle-) Matérn class of covariance functions. To this…
Kernel interpolation in Sobolev spaces of hybrid regularity
M. Griebel, H. Harbrecht
Kernel interpolation in tensor product reproducing kernel Hilbert spaces allows for the use of sparse grids to mitigate the curse of the dimension. Typically, besides the generic c…
Kernel interpolation on generalized sparse grids
Michael Griebel, Helmut Harbrecht, Michael Multerer
We consider scattered data approximation on product regions of equal and different dimensionality. On each of these regions, we assume quasi-uniform but unstructured data sites and…
On the Compressibility of Integral Operators in Anisotropic Wavelet Coordinates
Helmut Harbrecht, Remo von Rickenbach
The present article is concerned with the s*-compressibility of classical boundary integral operators in anisotropic wavelet coordinates. Having the s*-compressibility at hand, one…
Samplets: Wavelet concepts for scattered data
Helmut Harbrecht, Michael Multerer
This chapter is dedicated to recent developments in the field of wavelet analysis for scattered data. We introduce the concept of samplets, which are signed measures of wavelet typ…
On Sobolev and Besov Spaces of Hybrid Regularity
Helmut Harbrecht, Remo von Rickenbach
The present article is concerned with the nonlinear approximation of functions in the Sobolev space H^q with respect to a tensor-product, or hyperbolic wavelet basis on the unit n-…
On Quasi-Localized Dual Pairs in Reproducing Kernel Hilbert Spaces
Helmut Harbrecht, Rüdiger Kempf, Michael Multerer
In scattered data approximation, the span of a finite number of translates of a chosen radial basis function is used as approximation space and the basis of translates is used for…
The dimension weighted fast multipole method for scattered data approximation
Helmut Harbrecht, Michael Multerer, Jacopo Quizi
The present article is concerned scattered data approximation for higher dimensional data sets which exhibit an anisotropic behavior in the different dimensions. Tailoring sparse p…