Re: Precision issues
- To: mathgroup at smc.vnet.net
- Subject: [mg73516] Re: Precision issues
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Wed, 21 Feb 2007 01:39:06 -0500 (EST)
- Organization: The Open University, Milton Keynes, UK
- References: <erelv2$7ol$1@smc.vnet.net>
mickey 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?
You are using machine-precision numbers; therefore you cannot know
since, "Machine numbers, [...], always contain the same number of
digits, and maintain no information on their precision. [1]"
In[1]:=
sol = NIntegrate[Exp[-p^2 - q^2], {p, 0, 10},
{q, 0, 10}, Method -> MonteCarlo[24],
MaxPoints -> 1000000]
Out[1]=
0.7912492023745136
In[2]:=
Precision[sol]
Out[2]=
MachinePrecision
If you desire to be guarantee a specific level of precision, or at least
to know when Mahtematica failed to reach the desired precision, you must
use arbitrary-precision numbers. See the options PrcecisionGoal and
WorkingPrecision on the online help.
Regards,
Jean-Marc
[1] " The Mathematica Book Online / Advanced Mathematics in
Mathematica / Numbers / 3.1.4 Numerical Precision"
http://documents.wolfram.com/mathematica/book/section-3.1.4