Analytic Continuation by the Fast Fourier Transform

The ill-posed problem of analytic continuation is regularized by a prescribed bound. A simple computer algorithm is given that is based on the fast Fourier transform. The algorithm computes $m$ complex values and a positive error bound with time complexity $O(m\log m)$. As a function of the data errors and the prescribed bound, the numerical error is shown to be consistent with that prescribed by the three-circles principle of Hadamard.