FAST EVALUATION OF REAL AND COMPLEX EXPONENTIAL SUMS

Abstract

Recently, the butterfly approximation scheme and hierarchical approximations have been proposed for the efficient computation of integral transforms with oscillatory or asymptotically smooth kernels. Combining both approaches, we propose a certain fast Fourier-Laplace transform, which in particular allows for the fast evaluation of polynomials at nodes in the complex unit disk. All theoretical results are illustrated by numerical experiments.