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Re: Is it possible to make NIntegrate faster?

• To: mathgroup at smc.vnet.net
• Subject: [mg105204] Re: [mg105163] Is it possible to make NIntegrate faster?
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Tue, 24 Nov 2009 05:49:14 -0500 (EST)
• References: <200911231150.GAA21785@smc.vnet.net>
• Reply-to: drmajorbob at yahoo.com

You told us everything but what we need to know: the integrand.

It may be defined with SetDelayed, where Set could be much faster. There  
may be other issues.

But in a vacuum... who knows?

Bobby

On Mon, 23 Nov 2009 05:50:40 -0600, Leo Alekseyev <dnquark at gmail.com>  
wrote:

> Dear Mathgroup,
>
> Recently I have been using NIntegrate fairly extensively.  I am
> dealing with an oscillatory integral that has a singularity.
> NIntegrate is able to treat it reasonably well -- the only default I
> had to change was increasing MaxRecursion.  However, it is slow.  10
> points of my integrand take about 40 seconds to evaluate.  After I
> ported my code to another system, this same integral took about a second  
> using
> the Gauss-Kronrod method (quadgk in the other system).  Furthermore, by
> increasing the absolute and relative tolerance values, I could improve
> the speed without losing too much precision, so currently the
> integrals evaluate in 0.4 seconds.
>
> I have been playing with various NIntegrate parameters to try to
> improve the speed, to no effect.  My integrands are straightforward
> (although long) algebraic expressions involving a few Bessel functions
> and exponentials, wrapped inside a Module; all subexpressions use N[]
> so that nothing should be symbolic...  Ideally I hoped to find some
> sort of a speed/accuracy tradeoff, but that hasn't happened.
>
> I read the numerical integration tutorial in the docs, but am finding
> it hard to figure out how to improve the efficiency of my integration.
>  I would expect Mathematica to get to at least within an order of
> magnitude of the other system using the same integration strategy.  The  
> current
> performance isn't satisfactory -- but neither is the solution of
> porting perfectly good Mathematica code to the other system...
>
> I would much appreciate any suggestions.
>
> Thanks,
> --Leo
>


-- 
DrMajorBob at yahoo.com

• References:
  • Is it possible to make NIntegrate faster?
    • From: Leo Alekseyev <dnquark@gmail.com>