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Re: NIntegrate

• Subject: [mg3013] Re: NIntegrate
• From: rknapp (Robert Knapp)
• Date: 22 Jan 1996 05:54:34 -0600
• Approved: usenet@wri.com
• Distribution: local
• Newsgroups: wri.mathgroup
• Organization: Wolfram Research, Inc.
• Sender: mj at wri.com

Drib wrote:
> 
> Hi,
>         Could someone offer an indepth explaination about how
> NIntegrate achieves its results. I am currently using it to obtain
> some numerics for a comparison with results I have obtained analytically
> in my research. I feel I should know how they are obtained before
> relying on them.
> 
> All donations gratefully received
>                         Ian.

NIntegrate subdivides the interval of integration into subintervals.  
On each subinterval, it uses an approximation for the value of the
integral (by default, GaussKronrod, though through options, one can
specify a variety of methods).  An error estimate is made for each
subinterval and the total of the error estimates are added up to get 
the total error estimate.  Starting with the intervals with the largest
errors, the intervals are recursivly subdivided until the total error
estimate satisfies the values associates with the PrecisionGoal and
AccuracyGoal options, if possible.  

This is a very rough outline of how it works.  I suggest for more
information, you get the tutorial notes that Dave Wagner suggests.

Rob Knapp
WRI