A fast Laplace transform based on Laguerre functions

In this paper, we present a fast algorithm which evaluates a discrete Laplace transform with N points at M arbitrarily distributed points in C ( N + M ) C(N + M) work, where C depends only on the precision required. Our algorithm breaks even with the direct calculation at N = M = 20 N = M = 20 , and achieves a speedup of 1000 with 10000 points. It is based on a geometric divide and conquer strategy, combined with the manipulation of Laguerre expansions via a dilation formula for Laguerre functions.