Gräf, Manuel ; Kunis, Stefan : Stability results for scattered data interpolation on the rotation group

Author(s):

Gräf, Manuel
Kunis, Stefan

Title:

Stability results for scattered data interpolation on the rotation group

Electronic source:

application/pdf
application/postscript

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 27, 2007

Mathematics Subject Classification:

65T50			[ Discrete and fast Fourier transforms ]
65F10			[ Iterative methods for linear systems ]
43A75			[ Analysis on specific compact groups ]
41A05			[ Interpolation ]
15A60			[ Norms of matrices, numerical range, applications of functional analysis to matrix theory ]

Abstract:

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 log^2(N)+M) floating point operations.

Keywords:

scattered data interpolation, iterative methods, FFTs

Language:

English

Publication time:

12 / 2007