On the rate of convergence of the Gaver–Stehfest algorithm. (21st April 2021)

• Record Type: Journal Article
• Authors: Kuznetsov, Alexey; Miles, Justin
• Is Part Of: IMA journal of numerical analysis. Volume 42:Number 2(2022)
• Page Start: 1645
• Page End: 1664
• Publication Date: 2021-04-21
• Subjects: Gaver–Stehfest algorithm -- inverse Laplace transform -- rate of convergence -- Lambert W-function -- generating function; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/drab015
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: The Gaver–Stehfest algorithm is widely used for numerical inversion of the Laplace transform. In this paper we provide the first rigorous study of the rate of convergence of the Gaver–Stehfest algorithm. We prove that Gaver–Stehfest approximations converge exponentially fast if the target function is analytic in a neighbourhood of a point and they converge at a rate $o(n^{-k})$ if the target function is $(2k+3)$ -times differentiable at a point.