On the rate of convergence of the Gaver-Stehfest algorithm

Alexey Kuznetsov; Justin Miles

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arXiv · 2005.05813

On the rate of convergence of the Gaver-Stehfest algorithm

Alexey Kuznetsov·Justin Miles

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Abstract

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.

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Alexey Kuznetsov, Justin Miles. 2020-05-12. On the rate of convergence of the Gaver-Stehfest algorithm. https://arxiv.org/abs/2005.05813

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