Multiscale approximation for functions in arbitrary Sobolev spaces by scaled radial basis functions on the unit sphere

AbstractIn this paper, we prove convergence results for multiscale approximation using compactly supported radial basis functions restricted to the unit sphere, for target functions outside the reproducing kernel Hilbert space of the employed kernel

Polyharmonic approximation on the sphere

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 $L_p$ approximation order for this kind of approximation is $\sigma$ for functions having $L_p$ smoothness $\sigma$ (for $\sigma$ up to the order of the underlying differential operator, just as in univariate spline theory). This is an improvement over previous error estimates, which penalized the approximation order when measuring error in $L_p$, p>2 and held only in a restrictive setting when measuring error in $L_p$, p<2.Comment: 16 pages; revised version; to appear in Constr. Appro

Reorganisation der Arbeitsmarktpolitik Weiterbildung fuer Arbeitslose in Deutschland

UuStB Koeln(38)-940102218 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Continuous and discrete least-squares approximation by radial basis functions on spheres

AbstractIn this paper we discuss Sobolev bounds on functions that vanish at scattered points on the n-sphere Sn in Rn+1. The Sobolev spaces involved may have fractional as well as integer order. We then apply these results to obtain estimates for continuous and discrete least-squares surface fits via radial basis functions (RBFs). We also address a stabilization or regularization technique known as spline smoothing