Geodesic
Stability results for scattered data interpolation on the rotation group
Electronic transactions on numerical analysis, Tome 31 (2008), pp. 30-39
Fourier analysis on the rotation group $SO(3)$ 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 $SO(3)$, 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 N 3 Fourier coefficients from M well separated samples is shown to take only $O(N 3 log2 N + M )$ floating point operations.
Classification : 65T50, 65F10, 43A75, 41A05, 15A60
Keywords: scattered data interpolation, iterative methods, FFT 
@article{ETNA_2008__31__a20,
     author = {Gr\"af,  Manuel and Kunis,  Stefan},
     title = {Stability results for scattered data interpolation on the rotation group},
     journal = {Electronic transactions on numerical analysis},
     pages = {30--39},
     year = {2008},
     volume = {31},
     zbl = {1171.65105},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__31__a20/}
}
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AU  - Gräf,  Manuel
AU  - Kunis,  Stefan
TI  - Stability results for scattered data interpolation on the rotation group
JO  - Electronic transactions on numerical analysis
PY  - 2008
SP  - 30
EP  - 39
VL  - 31
UR  - http://geodesic.mathdoc.fr/item/ETNA_2008__31__a20/
LA  - en
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%A Gräf,  Manuel
%A Kunis,  Stefan
%T Stability results for scattered data interpolation on the rotation group
%J Electronic transactions on numerical analysis
%D 2008
%P 30-39
%V 31
%U http://geodesic.mathdoc.fr/item/ETNA_2008__31__a20/
%G en
%F ETNA_2008__31__a20
Gräf,  Manuel; Kunis,  Stefan. Stability results for scattered data interpolation on the rotation group. Electronic transactions on numerical analysis, Tome 31 (2008), pp. 30-39. http://geodesic.mathdoc.fr/item/ETNA_2008__31__a20/