MathGroup Archive 1992

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Re: Integrate.

  • To: mathgroup at
  • Subject: Re: Integrate.
  • From: David Withoff <withoff>
  • Date: Wed, 3 Jun 1992 17:14:19 -0500

> Perhaps it is noted already, but I have just noticed:
> If you DONT LOAD the patch to Integrate in the 2.0.4 Mac Standard version,
> you get speedups (about 1.8 faster and even more) both in Integrate
> and in NINTEGRATE !. 
> Have anyone (perhaps Jacobson) studied what happens if to do this, and why?
> A small explanation about how to acclerate NIntegrate would be a
> interesting document to let in the fileserver, by the way...
> -Alejandro Rivero

I wasn't able to reproduce this speed degradation for any integrals other
than ones directly affected by the "patch" (I presume you are referring
to the change in HypergeometricURule in the symbolic definite integration
code).  The code that gave the wrong answer is faster.  There are no
algorithmic links between Integrate and NIntegrate.  Any effect that
changes in Integrate might have on NIntegrate would have to work through
other channels, such as use of virtual memory. 

Regarding the question about speeding up NIntegrate, the best suggestion
is to study what NIntegrate does and select the appropriate options, etc.,
for the particular problem.  A description of how NIntegrate works and what
the options do is contained, among other places, in the notes for the
numerical computation mini-course and the numerical computation tutorial
from the 1992 Mathematica Conference.

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