Quality assurance of Gaver’s formula for multi-precision Laplace transform inversion in real case
Luisa D’Amore, Valeria Mele, Rosanna Campagna · Inverse Problems in Science and Engineering · 2017
We are concerned with Gaver’s formula, which is at the heart of a numerical algorithm, widely used in scientific and engineering applications, for computing approximations of inverse Laplace transform in multi-precision arithmetic systems. We demonstrate that, once parameters n (i.e. the number of terms of Gaver’s formula) and δ (i.e. an upper bound on noise on data) are given, then the number of correct significant digits of computed values of the inverse function is bounded above by -⌈log10(δ)⌉+1. In case of noise free data this number is arbitrarily large, as it is bounded below by n. We establish the requirement of the multi-precision system ensuring that the quality of numerical results is fulfilled. Experiments and comparisons validate the effectiveness of such approach.