Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 51, Issue 6, Pages 2984-2998Publisher
SIAM PUBLICATIONS
DOI: 10.1137/13091974X
Keywords
Gaver-Stehfest algorithm; inverse Laplace transform; Lambert W-function; generating functions; Dini criterion; Jordan criterion
Categories
Funding
- Natural Sciences and Engineering Research Council of Canada
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The Gaver-Stehfest algorithm for numerical inversion of Laplace transform was developed in the late 1960s. Due to its simplicity and good performance it is becoming increasingly more popular in such diverse areas as geophysics, operations research and economics, financial and actuarial mathematics, computational physics, and chemistry. Despite the large number of applications and numerical studies, this method has never been rigorously investigated. In particular, it is not known whether the Gaver-Stehfest approximations converge or what the rate of convergence is. In this paper we answer the first of these two questions: We prove that the Gaver-Stehfest approximations converge for functions of bounded variation and functions satisfying an analogue of Dini criterion.
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