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On the fast Fourier transform of functions with singularities. (English) Zbl 0838.65142
This paper gives a fast algorithm for the Fourier transform of functions with singularities. In particular, this paper contracts an algorithm for the fast Fourier transform on unequally spaced samples and tests its performance.
The number of operations required in this algorithm is $$O(N \log N + N_p (- \log \xi))$$ in one dimension, and $$O(N^2 \log N + N_p (- \log \xi)^2)$$ in two dimension, where $$N$$ is the number of computed frequencies, $$N_p$$ is the number of nodes, and $$\xi$$ is the precision of computation.

MSC:
 65T50 Numerical methods for discrete and fast Fourier transforms 65Y20 Complexity and performance of numerical algorithms
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