Re: Precision issues

*To*: mathgroup at smc.vnet.net*Subject*: [mg73537] Re: Precision issues*From*: Bill Rowe <readnewsciv at sbcglobal.net>*Date*: Wed, 21 Feb 2007 01:50:27 -0500 (EST)

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. -- To reply via email subtract one hundred and four