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We develop a new algorithm for the fast computation of discrete sums f (yⱼ): = ₊=₁N ₖ K (yⱼ-xₖ) (j =1,. . . , M) based on the recently developed fast Fourier transform (FFT) at nonequispaced knots. Our algorithm, in particular our regularization procedure, is simply structured and can be easily adapted to different kernels K. Our method utilizes the widely known FFT and can consequently incorporate advanced FFT implementations. In summary, it requires O (N N +M) arithmetic operations. We prove error estimates to obtain clues about the choice of the involved parameters and present numerical examples in one and two dimensions.
Potts et al. (Wed,) studied this question.