Least-squares determination of the inversion of Laplace transforms via Taylor series

Since the numerical inversion of Laplace transforms using Taylor series causes numerical instability owing to inversion of the Hilbert matrix, Unnikrishnan and Mathew recently proposed a technique to avoid the inversion of this ill-conditioned matrix. In the letter we show that improper use of their method could lead to very unreliable results. An implementation of their algorithm based on weighted least squares is also suggested.