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Is it possible to make NIntegrate faster?
- To: mathgroup at smc.vnet.net
- Subject: [mg105163] Is it possible to make NIntegrate faster?
- From: Leo Alekseyev <dnquark at gmail.com>
- Date: Mon, 23 Nov 2009 06:50:40 -0500 (EST)
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
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