Positive definite kernels are powerful tools for multivariate approximation from scattered data. This contribution discusses kernel-based image Radon To this end, we use weighted the reconstruction. Moreover, propose greedy algorithms, which used to adaptively select suitable spaces. reduces complexity of resulting reconstruction method and, moreover, it improves numerical stability quite signi...

This work proposes a nonparametric method to compare the underlying mean functions given two noisy datasets. The motivation for stems from an application of comparing wind turbine power curves. Comparing data presents new problems, namely need identify regions difference in input space and quantify extent that is statistically significant. Our proposed method, referred as funGP, estimates diffe...

Choosing models from a hypothesis space is frequent task in approximation theory and inverse problems. Cross-validation classical tool the learner's repertoire to compare goodness of fit for different reconstruction models. Much work has been dedicated computing this quantity fast manner but tackling its theoretical properties occurs be difficult. So far, most optimality results are stated an a...

This paper studies adaptive thinning strategies for approximating a large set of scattered data by piecewise linear functions over triangulated subsets. Our strategies depend on both the locations of the data points in the plane, and the values of the sampled function at these points — adaptive thinning. All our thinning strategies remove data points one by one, so as to minimize an estimate of...

Multistep interpolation of scattered data by compactly supported radial basis functions requires hierarchical subsets of the data. This paper analyzes thinning algorithms for generating evenly distributed subsets of scattered data in a given domain in IR. AMS subject classification: 41A15, 65D05, 65D07.

This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel B-splines are introduced to compute a C 2 -continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarse-tofine hierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function. Large p...

We discuss several approaches to the problem of interpolating or approximating data given at scattered points lying on the surface of the sphere. These include methods based on spherical harmonics, tensor-product spaces on a rectangular map of the sphere, functions deened over spherical triangulations, spherical splines, spherical radial basis functions, and some associated multi-resolution met...

This paper describes a new result on a wavelet scheme for scattered data interpolation extensively described in [2]. The interpolation scheme of [2] already has several advantages as compared to more classical RBF: it is highly stable and highly adaptive. In this paper, we describe a new property of this scheme: that the approximation error locally only depends on a local sample density or fill...