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MathGroup Archive 2005

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Re: Bug in MiniMaxApproximation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg60675] Re: Bug in MiniMaxApproximation
  • From: dh <dh at metrohm.ch>
  • Date: Sat, 24 Sep 2005 02:55:21 -0400 (EDT)
  • References: <dgtisl$25n$1@smc.vnet.net> <dh0f7t$qcn$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hallo Peter,
vielen Dank für Deine Antwort.
Weisst Du vielleicht ob es irgendwo eine allgemeine MiniMax Mathematica Routine 
gibt.
z.B. eine Mathematica Implementation des Remez or  Parks-McClellan algorithmus.
Gruss, Daniel

Moderator's rough translation -

Hello Peter -

Thank you for your answer.  Perhaps you know whether there is
a general MiniMax Mathematica routine e.g. a Mathematica
implementation of the Remez or Parks-McClellen alogrithms.

Thank you,  Daniel

Peter Pein wrote:
> dh schrieb:
> 
>>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
>>
> 
> Hi Daniel,
> 
> from the docs:
> "Because MiniMaxApproximation tries to minimize the maximum of the
> relative error, it is not possible to find a minimax approximation to a
> function that has a zero in the interval in question. "
> 
> 
> mm = x*MiniMaxApproximation[Piecewise[{{-1, x == 0}}, (1 - Exp[x])/x],
>  {x, {0, 2}, 1, 4}][[2,1]]
> 
> ((-1.0000021205528822 - 0.204709852011999*x)*x)/
>   (1 - 0.2952222393355634*x - 0.01939552534357132*x^2 +
>    0.017813878338228693*x^3 - 0.0020804136873956523*x^4)


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