The Bad Truth about Laplace's Transform

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 whos...

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Bibliographic Details
Published in:SIAM review 2008-09, Vol.50 (3), p.504-520
Main Authors: Epstein, Charles L., Schotland, John
Format: Article
Language:English
Subjects:
Approximation
Covariance
Exact sciences and technology
Fast Fourier transformations
Formulas (mathematics)
Fourier transformations
Fourier transforms
Ill posed problems
Information retrieval noise
Inverse
Laplace transformation
Laplace transforms
Mathematical analysis
Mathematical functions
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Noise
Noise measurement
Numerical analysis
Numerical analysis. Scientific computation
Operators
Problems and Techniques
Sciences and techniques of general use
Signal noise
Studies
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Summary: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.
ISSN:0036-1445
1095-7200
DOI:10.1137/060657273