5 citations · 16 across the 4 of their papers we have counts for
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Thinplate Splines on the Sphere
Rick K. Beatson, Wolfgang zu Castell
In this paper we give explicit closed forms for the semi-reproducing kernels associated with thinplate spline interpolation on the sphere. Polyharmonic or thinplate splines for ${\…
One-Step Recurrences for Stationary Random Fields on the Sphere
R. K. Beatson, W. zu Castell
Recurrences for positive definite functions in terms of the space dimension have been used in several fields of applications. Such recurrences typically relate to properties of the…
Dimension hopping and families of strictly positive definite zonal basis functions on spheres
R. K. Beatson, W. zu Castell
Positive definite functions of compact support are widely used for radial basis function approximation as well as for estimation of spatial processes in geostatistics. Several cons…
A Pólya criterion for (strict) positive definiteness on the sphere
R. K. Beatson, W. zu Castell, Y. Xu
Positive definite functions are very important in both theory and applications of approximation theory, probability and statistics. In particular, identifying strictly positive def…