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

**Follow-Ups**:**Re: Re: Is it possible to make NIntegrate***From:*DrMajorBob <btreat1@austin.rr.com>

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

**Re: Is it possible to make NIntegrate faster?***From:*DrMajorBob <btreat1@austin.rr.com>

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

**Re: Is it possible to make NIntegrate faster?***From:*DrMajorBob <btreat1@austin.rr.com>