Re: numeric inverse laplace transform of numeric data

• To: mathgroup at smc.vnet.net
• Subject: [mg21989] Re: numeric inverse laplace transform of numeric data
• From: Tom Pratum <pratum at u.washington.edu>
• Date: Thu, 10 Feb 2000 02:25:32 -0500 (EST)
• Organization: University of Washington
• References: <87b0g8\$o47@smc.vnet.net> <87e292\$s3o@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```John-
Thanks very much for your suggestion. For my application a FT wouldn't do. I
am trying to resolve a distribution of decaying exponentials into their
individual components. This is of course an old problem and has been attacked
in several different ways, probably the most successful numerical method to
date is a Fortran program called CONTIN written by Provencher at EMBO.
However, in theory a inverse Laplace transform would do the job, but you are
correct about the instability problems. I thought I would ask here to see if
anyone had written any kind of Mathematica Notebook to attack the problem,
since Mathematica is such a nice platform. Never hurts to ask.

Tom Pratum

John Doty wrote:

> Why not use the Fourier transform? It has properties analogous to the
> Laplace transform: you may think of it as the Laplace transform flipped
> over on its side in the complex plane. It is appropriate for the same
> sorts of jobs.
>
> Note that the path integral method of analytically inverting the Laplace
> transform implicitly converts it to a Fourier transform, and then
> inverse Fourier transforms that!
>
> I've never seen the Laplace transform used numerically. I suspect this
> is because its inverse is numerically unstable. This does not, of
> course, impede its use analytically.
>
> Tom Pratum wrote:
> >
> > Is there a known way to perform a numeric inverse laplace transform on a
> > list (as opposed to a function) in Mathematica? The methods provided in
> > mathsource are aimed at functions as opposed to lists.
>
> --
> John Doty               "You can't confuse me, that's my job."
> Home: jpd at w-d.org
> Work: jpd at space.mit.edu

--

Tom Pratum
Dept of Chemistry
Box 351700
Univ of Washington
pratum at u.washington.edu
http://staff.washington.edu/pratum

```

• Prev by Date: Re: multiple subscripted variables in NDSolve; dsfun
• Next by Date: Re: Mapping of mapping functions in metadefinitons
• Previous by thread: Re: numeric inverse laplace transform of numeric data
• Next by thread: assumptions question