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Complex variable and regularization methods of inversion of the Laplace transform


Authors: D. D. Ang, John Lund and Frank Stenger
Journal: Math. Comp. 53 (1989), 589-608
MSC: Primary 65R10; Secondary 44A10
DOI: https://doi.org/10.1090/S0025-5718-1989-0983558-7
MathSciNet review: 983558
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Abstract: In this paper three methods are derived for approximating f, given its Laplace transform g on $ (0,\infty )$, i.e., $ \smallint_0^\infty {f(t)\exp ( - st)\,dt = g(s)} $. Assuming that $ g \in {L^2}(0,\infty )$, the first method is based on a Sinc-like rational approximation of g, the second on a Sinc solution of the integral equation $ \smallint_0^\infty {f(t)\exp ( - st)\,dt = g(s)} $ via standard regularization, and the third method is based on first converting $ \smallint_0^\infty {f(t)\exp ( - st){\mkern 1mu} dt = g(s)} $ to a convolution integral over $ \mathbb{R}$, and then finding a Sinc approximation to f via the application of a special regularization procedure to solve the Fourier transform problem. We also obtain bounds on the error of approximation, which depend on both the method of approximation and the regularization parameter.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1989-0983558-7
Keywords: Laplace transform, inversion
Article copyright: © Copyright 1989 American Mathematical Society

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