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MathGroup Archive 2005

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Re: Bug in MiniMaxApproximation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg60649] Re: Bug in MiniMaxApproximation
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Fri, 23 Sep 2005 04:19:53 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, U.K.
  • References: <dgtisl$25n$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

dh wrote:
> Hello,
> it seems to me that MiniMaxApproximation fails each time the given 
> function is zero at the beginning of the specified interval
> Consider an example from the Help:
> 
> MiniMaxApproximation[Exp[x],{x, {0, 2}, 2, 4}]
> 
> this works fine. However, if you change the function to 1-Exp[..]:
> 
> MiniMaxApproximation[1 - Exp[x], {x, {0, 2}, 2, 4}]
> 
> you get an 1/0 error.
> 
> sincerely, Daniel
> 
Daniel,

Since "[...] minimax approximation r(x) to a given function f(x) is the 
rational function of the given degree that minimizes the maximum value 
of the quantity | 1 - r(x) / f(x) | over the interval under 
consideration," it is no wonder that when f(0) == 0 you get a division 
by wero error.

Check the paragraph after the graphics "Out[7]":
http://documents.wolfram.com/mathematica/Add-onsLinks/StandardPackages/NumericalMath/Approximations.html

Regards,
/J.M.


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