# Fast Forward Laplace transform

There are examples for fast numerical inversion of the Laplace transforms. For example here: http://www.mathworks.com/matlabcentral/fileexchange/32824-numerical-inversion-of-laplace-transforms-in-matlab

My question is: are there implementations of Fast Laplace transform? For example if one takes and array of values $[a_1 \ldots a_n]$ and transforms then to $[b_1 \ldots b_n]$.

• Isn't the thing you linked to an implementation? So the answer is "yes". – David Ketcheson Apr 16 '15 at 11:46
• Please make difference between a forward an inverse transform. My question is about the forward transform. – Dimiter P Apr 16 '15 at 23:06
• @DavidKetcheson: Based on a very quick skim, the linked implementation does not appear to be "fast", since the algorithm it implements (onlinelibrary.wiley.com/doi/10.1002/(SICI)1099-1204(199805/…) does not make any claims about $O(N \log N)$ (or less) complexity. – Geoff Oxberry Sep 8 '15 at 21:14
• The algorithm uses FFT and IFFT + a series expansion so it is approximately $O ( N log N)$ – Dimiter P Sep 8 '15 at 21:58