Maintenance of precision in NIntegrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg60504] Maintenance of precision in NIntegrate*From*: "Alan" <info at optioncity.REMOVETHIS.net>*Date*: Sun, 18 Sep 2005 01:16:00 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

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

**Follow-Ups**:**Re: Maintenance of precision in NIntegrate***From:*Murray Eisenberg <murray@math.umass.edu>