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Re: Re: Precision of AiryAi[0.0]

• To: mathgroup at smc.vnet.net
• Subject: [mg103496] Re: [mg103479] Re: Precision of AiryAi[0.0]
• From: Mark McClure <mcmcclur at unca.edu>
• Date: Fri, 25 Sep 2009 05:57:02 -0400 (EDT)
• References: <200909241149.HAA29080@smc.vnet.net>

On Thu, Sep 24, 2009 at 8:37 AM, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrot=
e:
> No, the function is not returning a MachinePrecision number. For
> example, note this:
>  Precision[Nest[Sqrt, AiryAi[0.0], 10^3]]
>  316.985
>
> As you can see,  precision was considerably increased by nesting
> square roots.

Correct.  If the precision of x is the number $MachinePrecision rather than
the symbol MachinePrecision, then arbitrary precision arithmetic will kick
in for computations involving x and this will be quite slow compared to the
floating point computations used for MachinePrecision numbers.  More to
the point for my application, we see:

Precision[Nest[AiryAi, 0.0, 100]]
225.079

Mark

• References:
  • Re: Precision of AiryAi[0.0]
    • From: Bill Rowe <readnews@sbcglobal.net>