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Inverting the Laplace transform is a paradigm for exponentially ill-posed problems. For a class of operators, including the Laplace transform, we give forward and inverse formulae that have fast implementations using the fast Fourier transform. These formulae lead easily to regularized inverses whose effects on noise and filtered data can be precisely described. Our results give cogent reasons for the general sense of dread most mathematicians feel about inverting the Laplace transform.
finite Fourier transform, FFT, Laplace transform, spectral theory, SVD, regularized inverse
Epstein, C. L., & Schotland, J. C. (2008). The Bad Truth about Laplace's Transform. Retrieved from https://repository.upenn.edu/be_papers/123
Date Posted: 15 September 2008
This document has been peer reviewed.