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Re: Quite Upset with NIntegrate

  • To: mathgroup at
  • Subject: [mg54357] Re: Quite Upset with NIntegrate
  • From: ituran at
  • Date: Sat, 19 Feb 2005 02:32:00 -0500 (EST)
  • References: <cv08ak$j42$>
  • Sender: owner-wri-mathgroup at

My response to Anton appeared before his thread. So, I think it is
better to post my reply again.

Dear Anton,

Thank you for your interest. I am attaching the sample file that has
the integrand and the limits even though everything was carried out
Mathematica. Below I would like to respond to your questions/remarks

[contact the author to get the attachment - moderator]

On Tue, 15 Feb 2005, Anton Antonov wrote:
> Dear Ismail Turan,

> As some of the guys in the forum mentioned, it is difficult to answer
your question
> without more detailed information.

> Some questions/remarks:

> 1. From what field this integral comes from?

It is from high energy physics. I am calculating the branching ratio of
particle decaying into three particles two of which are off-shell so
it doubles my phase space from 2 to 4-dimension.

> 2. How you have entered the integrand in Mathematica? Have you
imported it
>    from, say, a FORTRAN file?

I did everything with Mathematica regardless of the warnings of my
colleagues about the questionable capability of Mathematica in
integrations(for higher dimensions especially).

> 3. Have you tested are your integrand and boundaries of integration
correctly implemented?

The integrand is checked especially in 2-dimension as a limit of
4-dimensional case and there is a full agreement with the literature
results. The modification coming to the integrand in 4-dimension is to
multipy it by two density functions which reduce to Dirac-Delta
in 2-dimensional limit. In addition to that, the limits in 4-dim are
modified quite simply as far as physics is concerned.

> 4. Using MaxPoints invokes the MonteCarlo method.
>    You might try QuasiMonteCarlo method -- it is as fast as
>    and has more deterministic nature.

I tried what you have suggested here and I got the same data points
when I
set MaxPoints to somevalue but  leave the "Method" option "Automatic".

> 5. The default option settings in NIntegrate invoke the
MultiDimensional integration method.
>    You might try using a Cartesian rule method with

This made the process very slow. I haven't been able to get one data
so far (within aproximately five hours).

Thank you very much again. I really appreciate all the help.

Best Regards,

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