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MathGroup Archive 2007

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Re: Precision issues

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73531] Re: Precision issues
  • From: "Ray Koopman" <koopman at sfu.ca>
  • Date: Wed, 21 Feb 2007 01:47:16 -0500 (EST)
  • References: <erelv2$7ol$1@smc.vnet.net>

On Feb 20, 3:27 am, mickey <m... at hotmail.com> wrote:
> Hi,
>
> I am calculating certain integrals numerically and get back a number.
> Now, is it possible to determine how many digits is that answer accurate
> to?
>
> E.g.,
>
> NIntegrate[ Exp[-p^2 - q^2], {p, 0, 10}, {q, 0, 10}, Method ->
>      MonteCarlo[24], MaxPoints -> 1000000]
>
> Gives,
>
> 0.791249
>
> How many digits is this answer accurate to?
>
> Thanks,
> -M

The correct answer (to six digits) is 0.785398,
so you have two acccurate digits.

>From the Mathematica Help Browser,
NIntegrate > Further Examples > MonteCarlo:

"If the AccuracyGoal and PrecisionGoal are set to Automatic, they
 will be set to 2 in the methods MonteCarlo and QuasiMonteCarlo,
 and to 6 in all other methods."



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