Re: NIntegrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg89213] Re: NIntegrate*From*: antononcube <antononcube at gmail.com>*Date*: Thu, 29 May 2008 07:05:55 -0400 (EDT)*References*: <g1j6fa$qn4$1@smc.vnet.net>

Please try Timing[Do[ NIntegrate[Sin[x], {x, 0., 1.}, Method -> {Automatic, "SymbolicProcessing" -> 0}], {k, 10000}]] On my MacBook Pro it takes less than a second using Mathematica 6.0.2 . You are right that version 5.2 uses a Gauss-Kronrod rule. The points setting though is Points->5, which means that the rule would have 5 Gauss points and 6 Kronrod points. Anton Antonov, Wolfram Research, Inc. On May 28, 4:51 am, Michael Weyrauch <michael.weyra... at gmx.de> wrote: > Hello, > > I evaluate in Mathematica 5.2 > > Timing[Do[NIntegrate[Sin[x], {x, 0., 1.}], {k, 10000}]] > > {1.516 Second, Null} > > Doing this on the same computer in Mathematica 6.0.2 > > Timing[Do[NIntegrate[Sin[x], {x, 0., 1.}], {k, 10000}]] > > {84.5, Null} > > which does not look like progress. > > I realize that Mathematica 6.0.2 may use much more sophisticated > techniques than 5.2, therefore, I directed it what I think Mathematica > 5.2 may use (??): > > Timing[Do[NIntegrate[Sin[x], {x, 0., 1.}, > Method -> {"GaussKronrodRule", "Points" -> 2, > "SymbolicProcessing" -> 0}], {= k, 10000}]] > > {21.391, Null} > > Still not very convincing in comparison to 5.2. > > What is going on here? And how can I direct Mathematica 6 to be as fast > as 5.2 in trivial cases as the example above? > > Michael Weyrauch