MathGroup Archive 1997

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Re: multi-dim integration

  • To: mathgroup at
  • Subject: [mg7879] Re: [mg7847] multi-dim integration
  • From: seanross at
  • Date: Thu, 17 Jul 1997 15:35:42 -0400
  • Sender: owner-wri-mathgroup at

Xiaodong Wang wrote:
> Hi, everyone,
> Could anyone please kindly advise me if
> Mathematica or any other software can
> numerically evaluate multi-dimensional
> integration?
> any suggestion is greatly appreciated.
> Xiaodong Wang

Mma does multi-dimensional symbolic and numeric integration quite well.
The only drawback is that for really weird expressions it is rather slow
since the routine is so general.  If speed is a priority and you have a
function or set of data that is ill-behaved in some way, writing your
own routine is better, but for 98% of the uses I run into, the built-in
routine is very good.

In response to the general question:  Any programming language (C,
Pascal, Basic, Fortran, Mathematica, MatLab etc.) is capable of doing
mutlidimensional numerical integration.  The only thing that varies is
the amount of coding you need to do to get the job done.  If your
problem is critical, I personally think it is a  mistake to use a
pre-written routine if you don't know how to write your own because you
will not be aware of the limitations inherent to any numerical
technique.  Mma's routine is very general and robust, but it can
occasionally be faked out by obtuse functions or data and return wrong
answers.  If you don't know how to recognize the conditions under which
that is likely to happen you could be sorry.

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