Volume 31, pp. 30-39, 2008.
Stability results for scattered data interpolation on the rotation group
Manuel Gräf and Stefan Kunis
Abstract
Fourier analysis on the rotation group expands each function into the
orthogonal basis of Wigner-D functions.
Recently, fast and reliable algorithms for the evaluation of finite expansion
of such type, referred to as nonequispaced FFT on , have become available.
Here, we consider the minimal norm interpolation of given data by Wigner-D
functions.
We prove bounds on the conditioning of this problem which rely solely on the
number of Fourier coefficients and the separation distance of the sampling
nodes.
The reconstruction of Fourier coefficients from well separated
samples is shown to take only floating point
operations.
Full Text (PDF) [155 KB],
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Key words
Scattered data interpolation, iterative methods, FFT.
AMS subject classifications
65T50, 65F10, 43A75, 41A05, 15A60.