Local error estimates for radial basis function interpolation of scattered data |
| |
Authors: | WU ZONG-MIN; SCHABACK ROBERT |
| |
Institution: |
Department of Mathematics, Fudan University, Shanghai 200433 People's Republic of China
Institut fr numerische und angewandte Mathematik, Universitt Gttingen Lotzestrae 1618, D-3400 Gttingen, FRG
|
| |
Abstract: | Introducing a suitable variational formulation for the localerror of scattered data interpolation by radial basis functions(r), the error can be bounded by a term depending on the Fouriertransform of the interpolated function f and a certain Krigingfunction, which allows a formulation as an integral involvingthe Fourier transform of . The explicit construction of locallywell-behaving admissible coefficient vectors makes the Krigingfunction bounded by some power of the local density h of datapoints. This leads to error estimates for interpolation of functionsf whose Fourier transform f is dominated by thenonnegative Fourier transform of (x) = (||x||) in the sense . Approximation orders are arbitrarily high for interpolationwith Hardy multiquadrics, inverse multiquadrics and Gaussiankernels. This was also proven in recent papers by Madych andNelson, using a reproducing kernel Hilbert space approach andrequiring the same hypothesis as above on f, which limits thepractical applicability of the results. This work uses a differentand simpler analytic technique and allows to handle the casesof interpolation with (r) = rs for s R, s > 1, s 2N, and(r) = rs log r for s 2N, which are shown to have accuracy O(hs/2) |
| |
Keywords: | |
本文献已被 Oxford 等数据库收录! |
|