Limitations of inversion of real-valued Laplace transforms

Limitations are illustrated by examples from [1]. For a limited precision of imput data, the inversion of real-valued Laplace transforms yields satisfactory results where the original function f(t) rapidly tends to a smooth and monotonic function as t→∞.

Two consecutive extrema of the exact inverse transfirm located at t1 and t2>t1 can be resolved only when

t2/t1>exp(π/r) [2] (**).

For double precision of input data r≈20.

In general r ≈ number_of_correct_digits_in_input * 4/3

It follows from (**) that oscillating functions of frequency ω can be inverted only for small t