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MathGroup Archive 1997

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Re: Absolute error calculation with math software

  • To: mathgroup at smc.vnet.net
  • Subject: [mg8909] Re: [mg8889] Absolute error calculation with math software
  • From: Daniel Lichtblau <danl>
  • Date: Thu, 2 Oct 1997 22:57:01 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Thomas Weber wrote:
> 
> I have access to Mathematica.
> Can anybody tell me how I can calculate the absolute error of a
> physical quantity when I have got the absolute errors of all function
> variables? Or has anybody got a library that can help me do it?
> 
> Thomas
> 
> Please reply by mail.


Interval arithmetic may do what you want. Example:

In[30]:=  Sin[Interval[{.9,1.1}]]
Out[30]= Interval[{0.783327, 0.891207}]

Two caveats:

(i) This method will require real values (this may change in a future
release).

(ii) In complicated expressions you may get overly conservative
estimates, in particular if there are dependent terms that cancel.
Mathematica will compute each interval independent of the others.


Daniel Lichtblau
Wolfram Research
danl at wolfram.com


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