Quality assurance of Gaver's formula for multi-precision Laplace transform inversion in real case. Issue 4 (3rd April 2018)

• Record Type: Journal Article
• Authors: D'Amore, Luisa; Mele, Valeria; Campagna, Rosanna
• Is Part Of: Inverse problems in science and engineering. Volume 26:Issue 4(2018)
• Page Start: 553
• Page End: 580
• Publication Date: 2018-04-03
• Subjects: Laplace transform -- real inversion -- multi-precision -- Gaver's formula; 45Y04 -- 65R32 -- 65Y04 -- 68W40; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2017.1322963
• Languages: English
• ISSNs: 1741-5977

Abstract

Abstract : 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 - ⌈ log 10 ( 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.