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We construct a fast algorithm for the computation of discrete Gauss transforms with complex parameters, capable of dealing with non equispaced points. Our algorithm is based on the fast Fourier transform at non equispaced knots and requires only Oh(N) arithmetic operations. [ABSTRACT FROM AUTHOR]

Radial functions are a powerful tool in many areas of multi-dimensional approximation, especially when dealing with scattered data. We present a fast approximate algorithm for the evaluation of linear combinations of radial functions on the sphere [InlineMediaObject not available: see fulltext.]. The approach is based on a particular rank approximation of the corresponding Gram matrix and fast algorithms for spherical Fourier transforms. The proposed method takes [InlineMediaObject not available: see fulltext.]( L) arithmetic operations for L arbitrarily distributed nodes on the sphere. In contrast to other methods, we do not require the nodes to be sorted or pre-processed in any way, thus the pre-computation effort only depends on the particular radial function and the desired accuracy. We establish explicit error bounds for a range of radial functions and provide numerical examples covering approximation quality, speed measurements, and a comparison of our particular matrix approximation with a truncated singular value decomposition. [ABSTRACT FROM AUTHOR]