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A fast algorithm for filtering and wavelet decomposition on the sphere. (English) Zbl 1030.65148
Summary: This paper introduces a new fast algorithm for uniform-resolution filtering of functions defined on the sphere. We use a fast summation algorithm based on nonequispaced fast Fourier tansforms, building on previous work that used fast multipole methods. The resulting algorithm performs a triangular truncation of the spectral coefficients while avoiding the need for fast spherical Fourier transforms. The method requires \(O(N^2\log N)\) operations for \(O(N^2)\) grid points.
Furthermore, we apply these techniques to obtain a fast wavelet decomposition algorithm on the sphere. We present the results of numerical experiments to illustrate the performance of the algorithms.

MSC:
65T60 Numerical methods for wavelets
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
65T50 Numerical methods for discrete and fast Fourier transforms
Software:
NFFT
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