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MathGroup Archive 2006

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Re: Singularity-handling transformation employed by NIntegrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71191] Re: Singularity-handling transformation employed by NIntegrate
  • From: "dimitris" <dimmechan at yahoo.com>
  • Date: Fri, 10 Nov 2006 06:37:48 -0500 (EST)
  • References: <eiut46$h63$1@smc.vnet.net>

I have searched a lot regarding numerical integration in mathematica.
The truth is there are not many sources out there. You can achieve more
things with experiment.

Even the (giant and amazing book; actually the whole series worth the
money!) Mathematica Guidebook for Numerics my M. Trott does not contain
much information about SingularityDepth (I hope I don't lose
anything!).
I copy an except from it...

"SingularityDepth is an option for NIntegrate that determines the
number of recursive subdivisions of the interval of integration near
the endpoints and specified internal points, before a transformation of
variables of the endpoints and the specified internal points is to be
performed (provided the required accuracy or precision has not yet been
achieved)."

Another place you might consult is the following link for a
presentation of the late Jery B. Keiper at
http://library.wolfram.com/infocenter/Conferences/4679/

There is a complete subsection regarding SingularityDepth
although it doesn't answer to your question about the transformation.

There is also a book called Elementary Numerical Computing with
Mathematica
(see here for more information
http://library.wolfram.com/infocenter/Books/3533/);
Maybe you could find some material there; personally, I don't have it.
But I think it is
out of print.

I hope someone else will be more informative;
I am also quite interested in the subject.

Regards
Dimitris


Andrew Moylan wrote:
> Hi all,
>
> Further to a previous question: Can anyone tell me what transformation
> NIntegrate employs when a singularity is detected (i.e., when the
> number of recursive subdivisions specified by SingularityDepth is
> reached)?
> 
> Cheers,
> Andrew


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