A TAME method for the Inverse Laplace Transform of tame functions

by Nikita Deniskin (Scuola Normale Superiore)

Tuesday 31 Mar 2026, 11:00 → 12:00 Europe/Rome

Aula Magna (Dipartimento di Matematica)

The Laplace transform and its inverse are widely used tools in both theoretical and applied contexts. However, while the direct Laplace transform is stable, the inverse Laplace transform is an inherently ill-posed problem, which makes its accurate computation challenging;  this has led to extensive research in numerical methods for the inverse Laplace transform.

In this talk, we focus on a family of algorithms, called Abate-Whitt methods, which recover the original function via linear combinations of evaluations of the transform.
We relate the accuracy, with theoretical bounds, of the Abate-Whitt method to an approximation problem: constructing a rational approximation of the exponential $e^z$ on certain domains of the complex plane.
We propose a new method, dubbed TAME, based on the AAA algorithm for rational approximation.

TAME is especially effective for problems in queueing theory, in particular in analyzing phase-type distributions (Markov chains), and in computing the first return times in fluid queues. Here evaluations of the Laplace transform are (relatively) expensive, so it is highly important to minimize the number of needed evaluations.

Joint work with Federico Poloni, arXiv:2510.14799.