[82] in mathematical software users group
Re: multiple integral & pari
daemon@ATHENA.MIT.EDU (bfischer@BOURBAKI.MIT.EDU)
Mon Apr 26 13:57:20 1993
From: bfischer@BOURBAKI.MIT.EDU
To: siman@BOURBAKI.MIT.EDU
Date: Mon, 26 Apr 1993 13:55:35 -0400 (EDT)
Cc: msug@Athena.MIT.EDU
In-Reply-To: <9304232127.AA06756@cayley> from "siman@math.mit.edu" at Apr 23, 93 05:27:20 pm
> Second, about numerical integration. I'd like to numerically integrate a
> function with 4 variables:
>
> \int_{ abs(x1), ... , abs(x4) <=1 } f(x1, ..., x4)
> I'm happy to use mathematica to do the calculation, but it doesn't seem to
> like multiple integral either...
Mathematica seems to be able to handle multivariable numerical integrals; look in the manual (reference section) under NIntegrate (and also under Integrate to see the format). If that doesn't work (and even if it does), you might want to try Monte Carlo integration. At first this sound questionable, but numerical integration is just a matter of averaging the function at a bunch of points; how to choose the points is the only issue. In dimensions greater than (or equal to?) 3, Monte Carlo works better in practice (and I think in theory) than procedures based on regularity assumptions. You may still get a wrong answer, but that's true in any case.
Bruce Fischer
