Re: Numerical inversion of the Laplace Transform: Potential ilaplace maybe?

[Stephen Montgomery-Smith]

On 02/04/2013 05:13 AM, Robert Durkacz wrote:
> On Sun, Feb 3, 2013 at 7:26 AM, Fernando <address@hidden> wrote:
> 
>> See attached a algorithm for computing the inversion of the Laplace
>> Transform, algorithm developed by my thesis supervisor JAC Weideman back in
>> the day and co authored by N. Trefethen. The user must still choose the
>> number of functions evaluations. Maybe someone can do some error truncation
>> to avoid manual selection of function evaluations.
> 
> I looked at the code and understood enough to know that the question I
> have is a little off-topic but I will ask it anyway. Suppose I have
> numerically evaluated the Laplace transform of some function of t and
> therefore have a big table of the transform for real values s. How can
> I invert this numerically? (Not by using any form of contour
> integration as Fernando's algorithm does, I think because this will
> ask for complex values of s.)

I asked about this many years ago on newsgroups like sci.math.research.
 I was told that it was a very ill-conditioned problem, in that a very
small numerical change to the Laplace Transform would probably result in
a huge change in the value of the function.

I was quite excited when I saw the heading "numerical inversion of
Laplace Transform," and I expected that someone had figured out a good
solution to the problem.  But then I looked at the code and saw that it
evaluated the function at complex values.