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MathGroup Archive 2005

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Re: Integration over polytop

  • To: mathgroup at smc.vnet.net
  • Subject: [mg61841] Re: Integration over polytop
  • From: "antononcube" <antononcube at gmail.com>
  • Date: Tue, 1 Nov 2005 00:39:29 -0500 (EST)
  • References: <200510280725.DAA08678@smc.vnet.net><djv2g4$o4f$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

NIntegrate in Version 5.1 and later handles piecewise integrands.

The computations might be slow if the inequalities are too complex. It
is better to simplify them if it is possible.

If low accuracy of the result is required MonteCarlo methods can be
used.

It would be better if the double infinite integration ranges are
restricted to a final ones. For example, NIntegrate splits {x,
-Infinity, Infinity}  into {x, -Infinity, 0} and {x, 0, Infinity}, and
if all ranges are double infinite the integration will be over too many
subregions. For the example given in the original post the number of
the initial subregions will be 2^n, n=4.

Anton Antonov,
Wolfram Research, Inc.


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