## Complex variable and regularization methods of inversion of the Laplace transform

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- by D. D. Ang, John Lund and Frank Stenger PDF
- Math. Comp.
**53**(1989), 589-608 Request permission

## 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

- © Copyright 1989 American Mathematical Society
- 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