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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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