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MathGroup Archive 1993

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Re: 2D Integration

  • To: mathgroup at yoda.physics.unc.edu, swolf
  • Subject: Re: 2D Integration
  • From: keiper
  • Date: Mon, 7 Jun 93 18:15:25 CDT

  > A while back I posted a question on 2D integration - i.e. is there a
  > good way to do this in Mma? It would be nice if WRI would make a
  > decent 2D or 3D integration routine (hint hint) -- the built in
  > Mma NIntegrate is much to slow for multiple integration involving
  > interpolating functions. 

It is not clear what is meant by "decent", but presumably the idea is
to sacrifice accuracy for speed.  The default options for NIntegrate
are set to give 6 digits (assuming machine precision calculations) in
the final result.  Moreover the estimate of the error is rather
conservative so you often get a relative error that is much less than
10^-6.

But that is no reason to consider NIntegrate[ ] "indecent".  As a user
you are perfectly free to choose a different AccuracyGoal or PrecisionGoal.
For example:

In[4]:= Timing[NIntegrate[Exp[-x+2 y^2],{x,-1,1},{y,0,1}]]

Out[4]= {2.53333 Second, 5.55742}

In[5]:= Timing[NIntegrate[Exp[-x+2 y^2],{x,-1,1},{y,0,1}, PrecisionGoal -> 1]]

Out[5]= {0.05 Second, 5.55705}

By asking for only the first digit of the result to be correct we get
a speedup by a factor of more than 50 and still achieve a relative error
of less than 0.007 percent.

Jerry B. Keiper
keiper at wri.com
Wolfram Research, Inc.


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