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MathGroup Archive 2000

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Re: WorkingPrecision

  • To: mathgroup at smc.vnet.net
  • Subject: [mg23893] Re: WorkingPrecision
  • From: Richard Fateman <fateman at cs.berkeley.edu>
  • Date: Thu, 15 Jun 2000 00:51:32 -0400 (EDT)
  • Organization: University of California, Berkeley
  • References: <8hsttj$dh0@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

I think this is the explanation:
when you have workingprecision-> 16 you are using
normal double precision floats, which behave as you
more or less expect.

When you set higher working precision, you get WRI's
made-up numerical world of non-standard arithmetic,
in which precision and accuracy may be apparently
lost every time you do arithmetic. Whoever wrote
NIntegrate fell into one of these traps.  To see how this
can hurt you, try
x=1.11111111111111111111
Do[x=2*x-x, {100}]
If[x==x+1, "You must be running Mathematica"]


Regards,
 Richard Fateman


Bernd Brandt wrote:
> 
> Dear members,
> 
> Is someone able to explain why Accuracy and Precision decrease when i increase WorkingPrecision ?
> 
> The following illustrates my question:
> 
> In:
> ni = NIntegrate[x Sqrt[x], {x, 0, 25}, AccuracyGoal -> 6, PrecisionGoal -> 6,
> WorkingPrecision -> 16, Compiled -> False]
> 
> In: Accuracy[ni]
>         Precision[ni]
> 
> Out: 13
> Out: 16
> 
> In:             ni - 1250
> OUt:  -1.506340140622342*10^-6
> 
> Doing the same with WorkingPrecision->32 will yield:
>          Accuracy[ni] returns  3
>          Precision[ni] returns 7
> And: ni-1250 now is less accurate: -0. 10^-4
> 
> I am puzzled at this. Any help or a reference is highly appreciated.
> 
> Does someone have a good reference on Accuracy, Precision, AccuracyGoal, PrecisionGoal and WorkingPrecision?
> 
> Thank you,
> Bernd Brandt


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