Journal
SIAM REVIEW
Volume 50, Issue 3, Pages 504-520Publisher
SIAM PUBLICATIONS
DOI: 10.1137/060657273
Keywords
finite Fourier transform; FFT; Laplace transform; spectral theory; SVD; regularized inverse
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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.
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