# The Noise Handling Properties of the Talbot Algorithm for Numerically Inverting the Laplace Transform

## TL;DR

This paper evaluates the noise robustness of three numerical Laplace inversion algorithms, finding that the Talbot method significantly outperforms Fourier Series and Stehfest schemes in handling noisy data, making it advantageous for solving time-dependent differential equations.

## Contribution

The paper provides a comparative analysis of noise handling in Laplace inversion algorithms, highlighting the superior regularization properties of the Talbot method.

## Key findings

- Talbot algorithm handles noisy data effectively
- It outperforms Fourier Series and Stehfest methods
- Offers advantages for numerical solutions of differential equations

## Abstract

This paper examines the noise handling properties of three of the most widely used algorithms for numerically inverting the Laplace Transform. After examining the genesis of the algorithms, the regularization properties are evaluated through a series of standard test functions in which noise is added to the inverse transform. Comparisons are then made with the exact data. Our main finding is that the Talbot inversion algorithm is very good at handling noisy data and performs much better than the Fourier Series and Stehfest numerical inversion schemes as outlined in this paper. This offers a considerable advantage for it's use in inverting the Laplace Transform when seeking numerical solutions to time dependent differential equations.