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Re: Precision issues


On 2/20/07 at 6:21 AM, micky at hotmail.com (mickey) wrote:

>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?

2 digits.

The documentation for NIntegrate indicates the precision goal
and accuracy defaults to 2 when the integration method is
specified to MonteCarlo.

Note, on my machine

In[6]:=
NIntegrate[Exp[-p^2-q^2],{p,0,10},{q,0,10}]

Out[6]=
0.785398

returns a more accurate answer quicker than using the MonteCarlo
method with a large number of sample points.

And given

In[9]:=
Integrate[Exp[-p^2-q^2],{p,0,Infinity},{q,0,Infinity}]

Out[9]=
Pi/4

I am very confident the answer returned by NIntegrate with the
default options is more accurate than what is being returned
with the MonteCarlo method.

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