50 research outputs found
Direct and Inverse Results on Bounded Domains for Meshless Methods via Localized Bases on Manifolds
This article develops direct and inverse estimates for certain finite
dimensional spaces arising in kernel approximation. Both the direct and inverse
estimates are based on approximation spaces spanned by local Lagrange functions
which are spatially highly localized. The construction of such functions is
computationally efficient and generalizes the construction given by the authors
for restricted surface splines on . The kernels for which the
theory applies includes the Sobolev-Mat\'ern kernels for closed, compact,
connected, Riemannian manifolds.Comment: 29 pages. To appear in Festschrift for the 80th Birthday of Ian Sloa
Splines and Wavelets on Geophysically Relevant Manifolds
Analysis on the unit sphere found many applications in
seismology, weather prediction, astrophysics, signal analysis, crystallography,
computer vision, computerized tomography, neuroscience, and statistics.
In the last two decades, the importance of these and other applications
triggered the development of various tools such as splines and wavelet bases
suitable for the unit spheres , and the
rotation group . Present paper is a summary of some of results of the
author and his collaborators on generalized (average) variational splines and
localized frames (wavelets) on compact Riemannian manifolds. The results are
illustrated by applications to Radon-type transforms on and
.Comment: The final publication is available at http://www.springerlink.co
Refined error estimates for radial basis function interpolation
No description supplie