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Re: Precision of calculations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109469] Re: Precision of calculations
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Wed, 28 Apr 2010 02:00:41 -0400 (EDT)

If Abs[f'[x]] > 1, then f[x] has LESS precision than x.

If x is machine precision, there's no tracking of that loss of precision,  
so you could end up with no meaningful digits without knowing it.

If x is "arbitrary precision", there IS tracking... but it tends to be  
pessimistic. You might lose precision (according to Mathematica) even  
though -1 < f'[x] < 1. In that case, you lose precision but shouldn't.

Bobby

On Tue, 27 Apr 2010 03:04:32 -0500, Jim Lambaugh <lambaugh at gmail.com>  
wrote:

> Hi guys
>
> When I write numbers in my code, I do it as (e.g.)
>
> 1.0
> 1000.0
> Pi //N
> etc...
>
> Is it correct to say that my calculations are done with machine-
> precision, i.e. with rougly 16 digit precision?
>
> Regards,
> Jim.
>


-- 
DrMajorBob at yahoo.com


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