Algorithms for unequally spaced fast Laplace transforms

Fast algorithms for unequally spaced discrete Laplace transforms are presented. The algorithms are approximate up to a prescribed choice of computational precision, and they employ modified versions of algorithms for unequally spaced fast Fourier transforms using Gaussians. Various configurations of sums with equally and unequally spaced points can be dealt with. In contrast to previously presented fast algorithms for fast discrete Laplace transforms, the proposed algorithms are not restricted to the case of real exponentials but can deal with oscillations caused by complex valued nodes. Numerical experiments show that the computational complexity is comparable to that of computing ordinary discrete Fourier transforms by means of FFT. Results are given for the one-dimensional case, but it is straightforward to generalize them to arbitrary dimensions.