On the rate of convergence of the Gaver-Stehfest algorithm

05/12/2020

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by   Alexey Kuznetsov, et al.

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The Gaver-Stehfest algorithm is widely used for numerical inversion of 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.