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MathGroup Archive 2005

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Re: Maintenance of precision in NIntegrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg60516] Re: [mg60504] Maintenance of precision in NIntegrate
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Mon, 19 Sep 2005 04:45:36 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200509180516.BAA02315@smc.vnet.net>
  • Reply-to: murray at math.umass.edu
  • Sender: owner-wri-mathgroup at wolfram.com

You may want to set option WorkingPrecision as well.

Alan wrote:
> Consider integrating a function arg[] with a stated PrecisionGoal, say 10:
> 
> NIntegrate[arg[x], PrecisionGoal->10, ...]
> 
> The integrand arg[x] is a numerical function of the form:
> 
> arg[x] := (bunch of elementary functions) + NIntegrate[arg2[y],...]
> 
> arg2[y] is, at best, computable to MachinePrecision.
> 
> However, I don't know the best choices for
> PrecisionGoal or related options for the second integral (the inside 
> integral)
> in order to minimize my computation runtime. So, let's assume I do not use
> these options at all in the inside integral.
> 
> My question: will Mathematica then automatically request the inside
> integral to perform at a high enough PrecisionGoal in order to
> meet my PrecisionGoal target of 10 in the first (outside) integral?
> 
> Thanks,
> alan
> 
>  
> 
> 
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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