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A fast spherical filter with uniform resolution. (English) Zbl 0885.65016
The authors develop a fast algorithm for obtaining uniform resolution representation of a function known at a latitude-longitude grid on the surface of a sphere, equivalent to a triangular, isotropic truncation of the special harmonic coefficients for the function. This algorithm is based on the fast multipole method and the fast Fourier transform.
The proposed method projects the function to a space with uniform resolution while avoiding surface harmonic transformations. This method requires \(O(N^2\log N)\) operations for \(O(N^2)\) grid points, as proposed to \(O(N^3)\) operations for the standard spectral transform method, providing a reduced complexity spectral method obviating the pole problem in the integration of time-dependent partial differential equations on the sphere. The filter’s performance is demonstrated by numerical examples.
Reviewer: P.Narain (Bombay)

65D20 Computation of special functions and constants, construction of tables
65T50 Numerical methods for discrete and fast Fourier transforms
Full Text: DOI
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